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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsassumedInReverseRecapitalizationInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsassumedInReverseRecapitalizationInPeriodWeightedAverageExercisePrice</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsAmortization_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred Tax Assets, Tax Deferred Expense, Reserves and Accruals, Amortization</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, purchase price of common stock, percent</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Warrants</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Weighted Average Exercise Price</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionSharePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition, Share Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionSharePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Asset acquisition, share price.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionSharePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition, stock price per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt issuance costs, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Issuance Costs, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Issuance Costs, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsNet_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net of discount and issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodOfAutomaticIncreaseToOutstandingStockMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-based Compensation Arrangement by Share-based Payment Award, Period of Automatic Increase to Outstanding Stock Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodOfAutomaticIncreaseToOutstandingStockMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share-based Compensation Arrangement by Share-based Payment Award, Period of Automatic Increase to Outstanding Stock Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodOfAutomaticIncreaseToOutstandingStockMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, period of automatic increase to outstanding stock maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Significant Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property, Plant and Equipment [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheCTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche C term loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheCTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche C Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheCTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tranche C Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Grants in Period, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Granted (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementStrategyAndGovernanceTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management, Strategy, and Governance [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Basis in Diluted Net Loss Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfPre-FundedWarrantShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance Of Pre-Funded Warrant Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfPre-FundedWarrantShares_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance of pre-funded warrant shares.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfPre-FundedWarrantShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of pre-funded warrants (net of issuance cost) (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net loss per share attributable to common stockholders - basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share of common stock and pre-funded warrants, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NoncashInterestAndOtherExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncash interest and other expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NoncashInterestAndOtherExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash interest and other expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NoncashInterestAndOtherExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncash interest and other expense, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retirement Benefits [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PensionAndOtherPostretirementBenefitsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Retirement Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Outstanding at end (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Outstanding at beginning (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PatentCostsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Patent Costs, Policy</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PatentCostsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Patent Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PatentCostsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Patent Costs, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_EmploymentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employment Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_EmploymentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Employment agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_EmploymentAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Angel Employment Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustments to reconcile net loss to net cash used in operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Five</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2030</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsPayableDateOfRecordDayMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Dividend record date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsPayableDateOfRecordDayMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends Payable, Date of Record</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DomesticCountryMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Domestic Tax Jurisdiction [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalCashFlowElementsOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Cash Flow Elements, Operating Activity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalCashFlowElementsOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash operating activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DebtInstrumentNumberOfTranches_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of tranches</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DebtInstrumentNumberOfTranches_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Number of Tranches</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DebtInstrumentNumberOfTranches_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt Instrument, Number of Tranches</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Payments of debt issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments of Debt Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings (Accumulated Deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Retained Earnings (Accumulated Deficit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsTaxDeferredExpenseCompensationAndBenefitsShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Tax Deferred Expense, Compensation and Benefits, Share-Based Compensation Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ErigenAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Erigen Assets [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ErigenAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Erigen assets.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ErigenAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Erigen Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityWellKnownSeasonedIssuer_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Well-known Seasoned Issuer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityWellKnownSeasonedIssuer_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Well-known Seasoned Issuer</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Forfeitures in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Forfeitures in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Cancelled and forfeited (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsForfeituresInPeriod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Cancelled and forfeited (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Price Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockPricePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock price (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrepaidResearchAndDevelopmentCostsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid research and development costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrepaidResearchAndDevelopmentCostsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Research and Development Costs, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrepaidResearchAndDevelopmentCostsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Prepaid Research and Development Costs, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition Transaction Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Asset acquisition transaction costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition transaction costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss Contingencies [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingencies [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">At statutory rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationIncomeTaxExpenseBenefitAtFederalStatutoryIncomeTaxRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation at Federal Statutory Income Tax Rate, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Number of Securities Called by Warrants or Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Warrants issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net Loss Per Share Attributable to Common Stockholders</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerSharePolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities and stockholders' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Postal Zip Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash used in operating activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Operating Lease Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmProfitLossMeasureHowUsedDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Profit (Loss) Measure, How Used, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskRoleOfManagementTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Role of Management [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxCreditCarryforwardAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax credit carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxCreditCarryforwardAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Credit Carryforward, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Defined Contribution Plan, Employer Discretionary Contribution Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DefinedContributionPlanEmployerDiscretionaryContributionAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Defined contribution plan, employer discretionary contribution amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangements by Share-based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Granted (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Less accumulated depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ScheduleOfEstimatedUsefulLivesOfPropertyPlantAndEquipmentPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of estimated useful lives of property, plant and equipment [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ScheduleOfEstimatedUsefulLivesOfPropertyPlantAndEquipmentPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of estimated useful lives of property, plant and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ScheduleOfEstimatedUsefulLivesOfPropertyPlantAndEquipmentPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Estimated Useful Lives of Property, Plant and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Total gross deferred tax liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Tax Liabilities, Gross, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateImmaterialEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change in Accounting Principle, Accounting Standards Update, Immaterial Effect [true false]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedPaymentAwardStockOptionsValuationAssumptionsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Payment Award, Stock Options, Valuation Assumptions [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskMateriallyAffectedOrReasonablyLikelyToMateriallyAffectRegistrantFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Materially Affected or Reasonably Likely to Materially Affect Registrant [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental disclosure of cash flow information:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Cash Flow Information [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total gross deferred tax assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskBoardCommitteeOrSubcommitteeResponsibleForOversightTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Board Committee or Subcommittee Responsible for Oversight [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IncomeTaxReconciliationNonDeductibleExpenseTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IncomeTaxReconciliationNonDeductibleExpenseTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Reconciliation Non deductible Expense Transaction Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IncomeTaxReconciliationNonDeductibleExpenseTransactionCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Income Tax Reconciliation Non deductible Expense Transaction Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Information About Stock Options Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestOutstandingTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Vested and Expected to Vest, Outstanding [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income taxes paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Taxes Paid, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxesPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income Taxes Paid, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskProcessForInformingBoardCommitteeOrSubcommitteeResponsibleForOversightTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Process for Informing Board Committee or Subcommittee Responsible for Oversight [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net increase in cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Excluding Exchange Rate Effect, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive securities excluded from computation of earnings</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalShareBasedCompensationStockOptionsRequisiteServicePeriodRecognition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalShareBasedCompensationStockOptionsRequisiteServicePeriodRecognition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">APIC, Share-Based Payment Arrangement, Option, Increase for Cost Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, par value (in dollars per share)</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Warrants</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedActivitiesInitiationDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring and Related Activities, Initiation Date</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NetProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net proceeds from sales of common stock</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NetProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Net proceeds from issuance of common stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestructuringAndRelatedActivitiesCompletionDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring and Related Activities, Completion Date</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Exercised (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Exercised (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RestructuringAndRelatedCostNumberOfFullTimeEmployees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restructuring And Related Cost Number Of Full Time Employees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RestructuringAndRelatedCostNumberOfFullTimeEmployees_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Restructuring and related cost number of full time employees.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RestructuringAndRelatedCostNumberOfFullTimeEmployees_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of full time employees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ScheduleOfPrepaidExpensesAndOtherCurrentAssetTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Prepaid Expenses And Other Current Asset [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ScheduleOfPrepaidExpensesAndOtherCurrentAssetTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule Of Prepaid Expenses And Other Current Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ScheduleOfPrepaidExpensesAndOtherCurrentAssetTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Prepaid Expenses and Other Current Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses and other liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Long-term Debt Instruments [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Long-Term Debt Instruments [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByBalanceSheetGroupingTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, by Balance Sheet Grouping [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByBalanceSheetGroupingTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, by Balance Sheet Grouping [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AmendedAndRestatedTwoThousandTwentyThreeEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amended and Restated 2023 Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AmendedAndRestatedTwoThousandTwentyThreeEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amended and Restated Two Thousand Twenty Three Equity Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AmendedAndRestatedTwoThousandTwentyThreeEquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amended and restated two thousand twenty three equity incentive plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Preferred Stock, Shares Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Preferred Stock, Shares Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpensePolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and Development Expense and Accrued Research and Development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpensePolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Capital Shares Reserved for Future Issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, capital shares reserved for future issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementGeographicalAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statement Geographical Axis [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_StatementGeographicalAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Geographical [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Deferred Tax Assets and Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDeferredTaxAssetsAndLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Deferred Tax Assets and Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IncomeTaxReconciliationNonDeductibleExpenseTransactionCostsPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Reconciliation Non Deductible Expense Transaction Costs Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IncomeTaxReconciliationNonDeductibleExpenseTransactionCostsPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Income Tax Reconciliation Non Deductible Expense Transaction Costs Percent.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IncomeTaxReconciliationNonDeductibleExpenseTransactionCostsPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Transaction costs, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_JefferiesLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Jefferies LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_JefferiesLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Jefferies LLC [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_JefferiesLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Jefferies LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LitigationReserveCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued legal settlement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LitigationReserveCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Estimated Litigation Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Additional Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, number of additional shares issuable in period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsResearch_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and development tax credits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsTaxCreditCarryforwardsResearch_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Tax Credit Carryforwards, Research</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other noncurrent assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest Expense, Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StateAndLocalJurisdictionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">State and Local Jurisdiction [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCompensationCostForShareBasedPaymentArrangementsAllocationOfShareBasedCompensationCostsByPlanTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Stock Based Compensation Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfCompensationCostForShareBasedPaymentArrangementsAllocationOfShareBasedCompensationCostsByPlanTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Cost by Plan [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncash lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NoncashLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncash lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtExtinguishmentCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payment for Debt Extinguishment or Debt Prepayment Cost</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Maturity Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loan mature date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minimum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, share fair value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series A Warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A Warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series a warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Level 3</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AtTheMarketProgramMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">At-The-Market Program</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AtTheMarketProgramMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">At-The-Market Program [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AtTheMarketProgramMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">At-The-Market Program</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Fixed assets</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheATermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche A term loan.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Pre-FundedWarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pre-Funded Warrant [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Pre-FundedWarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Pre-Funded Warrant [Member].</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Pre-FundedWarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre-Funded Warrant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Pre-FundedWarrantMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">June 2025 Pre-Funded Warrant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NotSubjectToExpirationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Not Subject to Expiration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NotSubjectToExpirationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Not Subject to Expiration [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NotSubjectToExpirationMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Not Subject to Expiration</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromStockPlans_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from the issuance of common stock under equity plan awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromStockPlans_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Stock Plans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAJuniorParticipatingPreferredPurchaseRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Series A Junior Participating Preferred Purchase Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAJuniorParticipatingPreferredPurchaseRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series A Junior Participating Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAJuniorParticipatingPreferredPurchaseRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A Junior Participating Preferred Purchase Rights [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesAJuniorParticipatingPreferredPurchaseRightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series a junior participating preferred purchase rights.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and contingencies (Note 5)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Leases [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeasesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shareholders' Equity and Share-Based Payments [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareholdersEquityAndShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General and Administrative Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Present value of operating lease obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Present value of operating lease obligations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorFirmId_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Auditor Firm ID</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorFirmId_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Auditor Firm ID</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Basis Spread on Variable Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, basis spread on variable rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityReverseStockSplit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders' Equity, Reverse Stock Split</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityReverseStockSplit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reverse stock split</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in valuation allowance, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PurchaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Purchase Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PurchaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Purchase Agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PurchaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term Debt, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongtermDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementPositionsOrCommitteesResponsibleTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Positions or Committees Responsible [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loss Contingencies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LossContingenciesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loss Contingencies [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted-average shares used in computing basic net loss per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares used in computing basic net loss per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted-average shares used in computing basic net loss per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingExpenseInformationUsedByCodmDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, Expense Information Used by CODM, Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Effective Income Tax Rate Reconciliation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEffectiveIncomeTaxRateReconciliationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Effective Income Tax Rate Reconciliation [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Share-based Compensation Arrangements by Share-based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionEffectiveDateOfAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition, Effective Date of Acquisition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionEffectiveDateOfAcquisition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition, effective date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-Lived Tangible Asset [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Tangible Asset [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheBTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tranche B term loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheBTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tranche B Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TrancheBTermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tranche B Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskProcessForInformingManagementOrCommitteesResponsibleTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Process for Informing Management or Committees Responsible [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockExercisePriceOfWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Sale of stock, exercise price of warrants or rights.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockExercisePriceOfWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale Of Stock Exercise Price Of Warrants Or Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SaleOfStockExercisePriceOfWarrantsOrRights_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre-funded warrant price (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsNetAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Deferred tax assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsNetAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Net [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Events</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetPurchaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Purchase Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetPurchaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Asset purchase agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetPurchaseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset Purchase Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2026Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">O 2026 Q4 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2026Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">O 2026 Q4 dividends.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2026Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">O 2026 Q4 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Long-Term Debt, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-term debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateTerms_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Interest Rate Terms</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentInterestRateTerms_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument interest term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common stock warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock Warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonStockWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Change in Deferred Tax Assets Valuation Allowance, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in valuation allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Stockholders' Equity Attributable to Parent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Convertible preferred stock, par value (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Preferred stock, par or stated value per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis of Presentation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfAccountingPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Basis of Accounting, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Stockholders' Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_A2019And2017EquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">A 2019 and 2017 equity incentive plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_A2019And2017EquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">A2019 And2017 Equity Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_A2019And2017EquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2019 and 2017 Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SeriesAPreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series A Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SeriesAPreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series A Participating Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Use of Estimates</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UseOfEstimates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Use of Estimates, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leasehold improvements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leasehold Improvements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine2_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Address Line Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Measurements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DeferredTaxAssetsCapitalResearchAndDevelopment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred Tax Assets Capital Research And Development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DeferredTaxAssetsCapitalResearchAndDevelopment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets Capital Research And Development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DeferredTaxAssetsCapitalResearchAndDevelopment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Capitalized R&amp;D</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionSharesEquityInterestYetToBeIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition, stock to be issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionSharesEquityInterestYetToBeIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition Shares Equity Interest Yet To Be Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionSharesEquityInterestYetToBeIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Asset acquisition shares equity interest yet to be issued.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Accrued Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Accrued Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfUnrecognizedTaxBenefitsRollForwardTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Unrecognized Tax Benefits Roll Forward</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfUnrecognizedTaxBenefitsRollForwardTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Unrecognized Tax Benefits Roll Forward [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingCodmIndividualTitleAndPositionOrGroupOrCommitteeNameExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting, CODM, Individual Title and Position or Group Name [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plan Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAcceleratedVestingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Accelerated Vesting, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAcceleratedVestingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accelarated vesting of stock options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskMateriallyAffectedOrReasonablyLikelyToMateriallyAffectRegistrantTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Materially Affected or Reasonably Likely to Materially Affect Registrant [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementExpertiseOfManagementResponsibleTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Expertise of Management Responsible [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxPeriodAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax Period [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxPeriodAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Period [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingStandardsUpdateExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Standards Update [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesCommonStockSubjectToRepurchaseOrCancellation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: Weighted-average unvested restricted shares and shares subject to repurchase</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesCommonStockSubjectToRepurchaseOrCancellation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares, Common Stock Subject to Repurchase or Cancellation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesCommonStockSubjectToRepurchaseOrCancellation_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: Weighted-average unvested restricted shares and shares subject to repurchase</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AreaOfRealEstateProperty_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Area of real estate property</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AreaOfRealEstateProperty_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Area of Real Estate Property</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AreaOfRealEstateProperty_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Area of property (in sqft)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Reportable Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of reportable segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Property, Plant and Equipment, Gross, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Property, Plant and Equipment, Gross, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Property, Plant and Equipment, Gross, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_A2019EquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2019 Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_A2019EquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">2019 Equity Incentive Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_A2019EquityIncentivePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">2019 Equity Incentive Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CounterpartyNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Counterparty Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CounterpartyNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income (Loss) before provision for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsCurrentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net of discount and issuance costs, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsCurrentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Issuance Costs, Current, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredFinanceCostsCurrentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Issuance Costs, Current, Net, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedPaymentArrangementEmployeeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Payment Arrangement, Employee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedPaymentArrangementEmployeeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Employee [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash, cash equivalents and restricted cash at beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash, cash equivalents and restricted cash at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Warrant or Right, Exercise Price of Warrants or Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercise price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashOrPartNoncashAcquisitionFixedAssetsAcquired1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash or Part Noncash Acquisition, Fixed Assets Acquired</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoncashOrPartNoncashAcquisitionFixedAssetsAcquired1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment in accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title and Position [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsFairValueHierarchyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_IcfrAuditorAttestationFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">ICFR Auditor Attestation Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RemainedAvailableForIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Remained available for issuance of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RemainedAvailableForIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Remained Available for issuance of Common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RemainedAvailableForIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Remained available for issuance of cmmon stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted Stock Units</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedStockUnitsRSUMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Restricted Stock Units (RSUs) [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LesseeOperatingLeaseLiabilityToBePaidYearFourAndThereafter_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating Lease Liability to be Paid Year Four and Thereafter</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LesseeOperatingLeaseLiabilityToBePaidYearFourAndThereafter_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee operating lease liability to be paid year four and thereafter.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LesseeOperatingLeaseLiabilityToBePaidYearFourAndThereafter_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028 and beyond</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementClassOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementStrategyAndGovernanceLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management, Strategy, and Governance [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfPre-FundedWarrantValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance Of Pre-Funded Warrant Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfPre-FundedWarrantValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance of pre-funded warrant value.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfPre-FundedWarrantValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of pre-funded warrants (net of issuance cost)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumNumberOfSharesAvailableForGrantPerYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Share-based Compensation Arrangement by Share-based Payment Award, Maximum Number of Shares Available for Grant Per Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumNumberOfSharesAvailableForGrantPerYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share Based Compensation Arrangement By Share Based Payment Award Maximum Number Of Shares Available For Grant Per Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumNumberOfSharesAvailableForGrantPerYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, maximum number of shares available for grant per year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted-average shares used in computing diluted net loss per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Weighted-average shares used in computing diluted net loss per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares of common stock and pre-funded warrants outstanding, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Securities Act File Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRateMinimum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Volatility Rate, Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRateMinimum_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected volatility, Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalLeaseObligationsIncurred_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease Obligation Incurred</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalLeaseObligationsIncurred_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease modification</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Percentage of Outstanding Stock Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPercentageOfOutstandingStockMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, percentage of outstanding stock maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalBalanceSheetDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Balance Sheet Items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalBalanceSheetDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Balance Sheet Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SummaryOfValuationAllowanceTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Summary of Valuation Allowance [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SummaryOfValuationAllowanceTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Reconciliation of the Total Change in the Valuation Allowance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ThersholdIndexRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Thershold index rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ThersholdIndexRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">ThersholdIndexRate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ThersholdIndexRate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">ThersholdIndexRate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Operating Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of operating segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Sale of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Reporting</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and administrative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">General and Administrative Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxJurisdictionOfDomicileExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Jurisdiction of Domicile [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SignificantRisksAndUncertaintiesPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Risks and Uncertainties</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SignificantRisksAndUncertaintiesPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Significant Risks And Uncertainties, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SignificantRisksAndUncertaintiesPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Significant Risks And Uncertainties, Policy</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Shares Issued in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardSharesIssuedInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, shares issued in period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOther_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOther_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionMaximumFundingCommitment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition, maximum funding commitment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionMaximumFundingCommitment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition Maximum Funding Commitment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AssetAcquisitionMaximumFundingCommitment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Asset acquisition maximum funding commitment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_A2019EmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2019 Employee Stock Purchase Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_A2019EmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">2019 Employee Stock Purchase Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_A2019EmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">2019 Employee Stock Purchase Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rent expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AccruedClinicalTrialLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued clinical trial liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AccruedClinicalTrialLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AccruedClinicalTrialLiability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AccruedClinicalTrialLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">AccruedClinicalTrialLiability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Useful Life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLife_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property, plant and equipment, useful life</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recently Adopted Accounting Standards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Future Minimum Rental Payments under Operating Leases with Noncancelable Terms</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of shares purchase from preferred stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Conversion of Convertible Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, award vesting period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRateMinimum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate, Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRateMinimum_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Risk-free interest rate, Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Domestic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesDomestic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Domestic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Depreciation, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PercentageOfAnnualBonus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of annual bonus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PercentageOfAnnualBonus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage Of Annual Bonus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PercentageOfAnnualBonus_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of annual bonus.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Term of Contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Term of contract</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Common Stock, Shares, Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Common Stock, Shares, Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less: current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Current operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: current portion</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_BrisbaneCaliforniaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Brisbane California.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_BrisbaneCaliforniaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Brisbane California [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_BrisbaneCaliforniaMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Brisbane, California</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementProcessesIntegratedFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Processes Integrated [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net deferred tax assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsLiabilitiesNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_NoTradingSymbolFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">No Trading Symbol Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsStateAndLocal_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating loss carryforwards, state</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsStateAndLocal_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Operating Loss Carryforwards, State and Local</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfCashFlowsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Cash Flows [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Aggregate sales price of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock for cash (net of issuance cost)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Stock Options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Option, Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Share-Based Payment Arrangement, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpenseShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders' Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrivateTempestPreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Private tempest preferred stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrivateTempestPreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Private Tempest Preferred Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrivateTempestPreferredStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Private Tempest Preferred Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DeferredTaxLiabilitiesOperatingLeaseRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Right-of-use assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DeferredTaxLiabilitiesOperatingLeaseRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities, Operating Lease, Right-of Use Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DeferredTaxLiabilitiesOperatingLeaseRightOfUseAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred Tax Liabilities, Operating Lease, Right-of Use Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net Loss Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComputerEquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Computer equipment and software</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComputerEquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Computer Equipment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementProcessesIntegratedTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Processes Integrated [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net Income (Loss) Attributable to Parent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock Issuance Costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issuance Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_StockIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Dividends</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Dividend Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedDividendRate_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Assumed dividend yield</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Vested and Expected to Vest, Exercisable, Aggregate Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableAggregateIntrinsicValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Aggregate Intrinsic Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Risk-free interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Prepaid expenses and other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Repayments of Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Repayment of debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RepaymentsOfDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Repayment of loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrivateInvestmentInPublicEntityFinancingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Private investment in public entity financing.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrivateInvestmentInPublicEntityFinancingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Private Investment In Public Entity Financing [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PrivateInvestmentInPublicEntityFinancingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">PIPE Financing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CompensationAndRetirementDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retirement Benefits [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, fair value of stock options vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedInPeriodFairValue1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested in Period, Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Nonoperating</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest Expense, Nonoperating, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseNonoperating_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Interest expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Income before Income Tax, Domestic and Foreign [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfIncomeBeforeIncomeTaxDomesticAndForeignTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Income (Loss) Before Provision for Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and Development Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionDateOfAcquisitionAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition, Date of Acquisition Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionDateOfAcquisitionAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Asset acquisition, agreement date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research Tax Credit Carryforward</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research Tax Credit Carryforward [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Measurements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Measurement, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TemporaryEquityDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Temporary Equity Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Tax Reserve [Roll Forward]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReconciliationOfUnrecognizedTaxBenefitsExcludingAmountsPertainingToExaminedTaxReturnsRollForward_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits [Roll Forward]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IndividualsWhoWereNotPreviouslyEmployeesOrDirectorsOfCompanyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Individuals who were not Previously Employees or Directors of Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IndividualsWhoWereNotPreviouslyEmployeesOrDirectorsOfCompanyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Individuals Who Were Not Previously Employees or Directors Of Company [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IndividualsWhoWereNotPreviouslyEmployeesOrDirectorsOfCompanyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Individuals who were not previously employees or directors of company.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Consideration Received on Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockConsiderationReceivedOnTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Consideration received</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rights Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RightsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Rights [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Sale of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Class of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DebtInstrumentExitFee_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument Exit Fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DebtInstrumentExitFee_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt instrument exit fee.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_DebtInstrumentExitFee_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt instrument, exit fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash used in investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrivatePlacementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Private Placement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrivatePlacementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Private Placement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_CommonWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Common warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesNetAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Deferred tax liability:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxLiabilitiesNetAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Liabilities, Net [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationNondeductibleExpenseShareBasedCompensationCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Share-Based Payment Arrangement, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Cancelled and forfeited (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangements by Share-based Payment Award, Options, Forfeitures in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsForfeituresInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Forfeitures in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Income Taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesIssuedBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average common shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesIssuedBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Issued, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LegalEntityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Legal Entity [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LegalEntityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Legal Entity [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Changes in operating assets and liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Property and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Outstanding at end (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Outstanding at beginning (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Outstanding (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InsuranceSettlementsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Insurance recovery of legal settlement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InsuranceSettlementsReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Insurance Settlements Receivable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrecognizedTaxBenefits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrecognized Tax Benefits</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid-in Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional Paid-In Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses and other liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accrued Liabilities and Other Operating Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Measurement Frequency [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementFrequencyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Statement Location [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementLocationAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Income Location, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRateMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Risk Free Interest Rate, Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsRiskFreeInterestRateMaximum_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Risk-free interest rate, Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Nontaxable or nondeductible items, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationNondeductibleExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Effective Income Tax Rate Reconciliation, Nondeductible Expense, Percent, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Subsequent Event Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Event Type [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingPeriodIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Period Increase (Decrease)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingPeriodIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Period Increase (Decrease), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingPeriodIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share based compensation, modified stock options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PercentageOfCommissionOnSaleOfStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of commission on sale of stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PercentageOfCommissionOnSaleOfStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage Of Commission On Sale Of Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PercentageOfCommissionOnSaleOfStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of commission on sale of stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee-related Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Employee-related Liabilities, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected term (in years)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardFairValueAssumptionsExpectedTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Fair Value Assumptions, Expected Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Recurring</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total minimum lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PreFundedWarrantAndCommonWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pre Funded Warrant And Common Warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PreFundedWarrantAndCommonWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Pre funded&#160;warrant and common warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PreFundedWarrantAndCommonWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre Funded Warrant and Common Warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less: imputed interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Tax Credit, Research, Percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and development credit, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationTaxCreditsResearch_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Research and development credit, percent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Ecor1CapitalLlcAndVersantVentureCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">EcoR1 Capital LLC and Versant Venture Capital.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Ecor1CapitalLlcAndVersantVentureCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">EcoR1 Capital LLC And Versant Venture Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Ecor1CapitalLlcAndVersantVentureCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">EcoR1 Capital, LLC and Versant Venture Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Components [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Components [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsVestedAndExpectedToVestExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseExcludingAcquiredInProcessCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpenseExcludingAcquiredInProcessCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense (Excluding Acquired in Process Cost)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationArrangementWithIndividualAllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock compensation expense related to employees stock options grants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationArrangementWithIndividualAllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Compensation Arrangement with Individual, Allocated Share-Based Compensation Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other income (expense), net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Nonoperating Income (Expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByAssetClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentAnnualReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Annual Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentAnnualReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Annual Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PublicFloat_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Public Float</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PublicFloat_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Public float.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_PublicFloat_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Public float</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Employee Stock Purchase Plans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Purchase of shares of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Expiration Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, expiration period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockVotingRights_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Voting rights of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockVotingRights_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Voting Rights</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating loss carryforwards, federal</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsDomestic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Operating Loss Carryforwards, Domestic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Pre-FundedWarrantsIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pre-Funded Warrants Issuance Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Pre-FundedWarrantsIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Pre-funded warrants issuance cost.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_Pre-FundedWarrantsIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Pre-funded warrants issuance cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalCashFlowElementsInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Cash Flow Elements, Investing Activity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalCashFlowElementsInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash investing activities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfCommonStockValueUnderEquityPlanAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock under equity plan award</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfCommonStockValueUnderEquityPlanAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Issuance Of Common Stock Value Under Equity Plan Awards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IssuanceOfCommonStockValueUnderEquityPlanAwards_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Issuance of common stock value under equity plan awards.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangements by Share-based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Exercised (in dollars per share)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Prepaid Expense, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, $0.001 par value; 100,000,000 shares authorized; 4,927,161 and 3,382,432 shares issued and outstanding at December 31, 2025 and December 31, 2024, respectively</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Stockholders' Equity, Including Portion Attributable to Noncontrolling Interest, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total stockholders' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ProceedsFromIssuanceOfCommonStockWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from the issuance of common stock warrants, net of issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ProceedsFromIssuanceOfCommonStockWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds From Issuance Of Common Stock Warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ProceedsFromIssuanceOfCommonStockWarrants_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Proceeds from issuance of common stock warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Assumed in reverse recapitalization (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lab equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equipment [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net operating losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Tax Assets, Operating Loss Carryforwards</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Deferred Tax Assets, Operating Loss Carryforwards, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementProcessesForAssessingIdentifyingAndManagingThreatsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Processes for Assessing, Identifying, and Managing Threats [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxCreditCarryforwardAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax Credit Carryforward [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TaxCreditCarryforwardAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Tax Credit Carryforward [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Impairment of Long-Lived Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Impairment or Disposal of Long-Lived Assets, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_OperatingLeaseCommencementMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease Commencement Month And Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_OperatingLeaseCommencementMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Operating lease commencement month and year.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_OperatingLeaseCommencementMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease commencement month and year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpenseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other income (expense), net:</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityPublicFloat_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Public Float</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityPublicFloat_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Public Float</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardFairValueAssumptionsExpectedVolatilityRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected volatility</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock, shares authorized</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Disclosure [Text Block]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LegacyMillendoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Legacy Millendo</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LegacyMillendoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Legacy Millendo</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_LegacyMillendoMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Legacy Millendo [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentPeriodicPaymentPrincipal_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Monthly principal payments</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityVoluntaryFilers_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Voluntary Filers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityVoluntaryFilers_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Voluntary Filers</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest income and other income (expense), net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Nonoperating Income (Expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Nonoperating Income (Expense), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional paid-in capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Additional Paid in Capital, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsequentEventsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Subsequent Events [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="cyd_CybersecurityRiskManagementPositionsOrCommitteesResponsibleFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cybersecurity Risk Management Positions or Committees Responsible [Flag]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Provision for income taxes</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Expense (Benefit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Measurement Frequency [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByMeasurementFrequencyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Frequency [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Gross proceeds from issuance of common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from the issuance of common stock, net of issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TwoThousandTwentyThreeInducementPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2023 Inducement Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TwoThousandTwentyThreeInducementPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Three Inducement Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TwoThousandTwentyThreeInducementPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty three inducement plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Concentration of Credit Risk</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConcentrationRiskCreditRisk_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Concentration Risk, Credit Risk, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Purchase of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based compensation arrangement by share-based payment award, number of shares granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Term loan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Term Loan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_TermLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term Loan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property, Plant and Equipment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Exercisable, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableWeightedAverageRemainingContractualTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercisable, Weighted Average Remaining Contractual Term</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_WarrantsIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Warrants Issuance Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_WarrantsIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Warrants issuance cost.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_WarrantsIssuanceCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock warrants issuance cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IncomeTaxLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Income Tax Line Items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IncomeTaxLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income Tax [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_IncomeTaxLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock, Number of Shares Issued in Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Shares issued in transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Issuance of common stock for cash (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock for cash (net of issuance cost) (in shares)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Net loss per share attributable to common stockholders - diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareDiluted_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share of common stock and pre-funded warrants, diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableTrade_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableTrade_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accounts Payable, Trade</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_TitleOfIndividualWithRelationshipToEntityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title and Position [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetAcquisitionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Acquisition [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentUsefulLifeDescriptionOfTermExtensibleEnumeration_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant, and Equipment, Useful Life, Term, Description [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Auditor Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Auditor Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loan amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtInstrumentFaceAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Instrument, Face Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Line of Credit Facility, Maximum Borrowing Capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Borrowing capacity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2023Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">O 2023 Q4 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2023Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">O 2023 Q4 Dividends.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_O2023Q4DividendsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">O 2023 Q4 Dividends [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Counterparty Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationTaxCreditsResearch_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Tax Credit, Research, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationTaxCreditsResearch_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and development credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxReconciliationTaxCreditsResearch_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Research and development credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AnnualBaseSalary_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Annual Base Salary</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AnnualBaseSalary_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Annual base salary.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_AnnualBaseSalary_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Anual base salary</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesBWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Series B warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesBWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Series b warrants.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_SeriesBWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Series B warrants</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RegisteredDirectOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Registered Direct Offering [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RegisteredDirectOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Registered Direct Offering [Member].</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_RegisteredDirectOfferingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">RDO</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LetterOfCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Letter of Credit [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LetterOfCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Letter of Credit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and Cash Equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtPercentageBearingVariableInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt, Percentage Bearing Variable Interest, Percentage Rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebtPercentageBearingVariableInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Annual floating interest rate</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Property and equipment&#8212;net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment&#8212;net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based Compensation Arrangement by Share-based Payment Award, Options, Vested and Expected to Vest, Exercisable, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsVestedAndExpectedToVestExercisableNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Vested and Expected to Vest, Exercisable, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Income (Loss)</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NovemberTwoThousandTwentyFivePreFundedWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">November Two Thousand Twenty Five Pre Funded Warrants [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="tpst_NovemberTwoThousandTwentyFivePreFundedWarrantsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">November 2025 Pre-Funded Warrants.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Share-based payment arrangement, nonvested award, option, cost not yet recognized, amount</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AuditorOpinionTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Auditor Opinion [Text Block]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Policies [Abstract]</link:label>
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  <xsd:element id="tpst_AssetAcquisitionMaximumFundingCommitment" name="AssetAcquisitionMaximumFundingCommitment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_EmployeeStockOwnershipPlanMember" name="EmployeeStockOwnershipPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_DeferredTaxAssetsCapitalResearchAndDevelopment" name="DeferredTaxAssetsCapitalResearchAndDevelopment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_NoncashInterestAndOtherExpenseNet" name="NoncashInterestAndOtherExpenseNet" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_IncomeTaxLineItems" name="IncomeTaxLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_LegacyMillendoMember" name="LegacyMillendoMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_DeferredTaxLiabilitiesOperatingLeaseRightOfUseAssets" name="DeferredTaxLiabilitiesOperatingLeaseRightOfUseAssets" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_A2019EmployeeStockPurchasePlanMember" name="A2019EmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_IncomeTaxReconciliationNonDeductibleExpenseTransactionCosts" name="IncomeTaxReconciliationNonDeductibleExpenseTransactionCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_ProceedsFromIssuanceOfCommonStockWarrants" name="ProceedsFromIssuanceOfCommonStockWarrants" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_NovemberTwoThousandTwentyFivePreFundedWarrantsMember" name="NovemberTwoThousandTwentyFivePreFundedWarrantsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_SeriesAJuniorParticipatingPreferredPurchaseRightsMember" name="SeriesAJuniorParticipatingPreferredPurchaseRightsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_ScheduleOfPrepaidExpensesAndOtherCurrentAssetTableTextBlock" name="ScheduleOfPrepaidExpensesAndOtherCurrentAssetTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_RemainedAvailableForIssuanceOfCommonStock" name="RemainedAvailableForIssuanceOfCommonStock" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_StockIssuanceCosts" name="StockIssuanceCosts" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_A2019EquityIncentivePlanMember" name="A2019EquityIncentivePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_OperatingLeaseCommencementMonthAndYear" name="OperatingLeaseCommencementMonthAndYear" type="xbrli:gYearMonthItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestingDate" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestingDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodOfAutomaticIncreaseToOutstandingStockMaximum" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardPeriodOfAutomaticIncreaseToOutstandingStockMaximum" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_TwoThousandTwentyThreeInducementPlanMember" name="TwoThousandTwentyThreeInducementPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_IssuanceOfCommonStockValueUnderEquityPlanAwards" name="IssuanceOfCommonStockValueUnderEquityPlanAwards" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_NotSubjectToExpirationMember" name="NotSubjectToExpirationMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_TrancheCTermLoanMember" name="TrancheCTermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_Pre-FundedWarrantsIssuanceCost" name="Pre-FundedWarrantsIssuanceCost" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_DeferredTaxAssetsOperatingLeaseLiability" name="DeferredTaxAssetsOperatingLeaseLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_ScheduleOfEstimatedUsefulLivesOfPropertyPlantAndEquipmentPolicyTextBlock" name="ScheduleOfEstimatedUsefulLivesOfPropertyPlantAndEquipmentPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_AssetPurchaseAgreementMember" name="AssetPurchaseAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_PreFundedWarrantAndCommonWarrantsMember" name="PreFundedWarrantAndCommonWarrantsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_IssuanceOfCommonStockSharesUnderEquityPlanAwards" name="IssuanceOfCommonStockSharesUnderEquityPlanAwards" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_RegisteredDirectOfferingMember" name="RegisteredDirectOfferingMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_NetProceedsFromIssuanceOfCommonStock" name="NetProceedsFromIssuanceOfCommonStock" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_PercentageOfAnnualBonus" name="PercentageOfAnnualBonus" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_BrisbaneCaliforniaMember" name="BrisbaneCaliforniaMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_PatentCostsPolicyPolicyTextBlock" name="PatentCostsPolicyPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_DebtInstrumentNumberOfTranches" name="DebtInstrumentNumberOfTranches" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="tpst_PercentageOfCommissionOnSaleOfStock" name="PercentageOfCommissionOnSaleOfStock" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_ThersholdIndexRate" name="ThersholdIndexRate" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="tpst_SaleOfStockExercisePriceOfWarrantsOrRights" name="SaleOfStockExercisePriceOfWarrantsOrRights" type="xbrli:decimalItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="tpst_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsassumedInReverseRecapitalizationInPeriodWeightedAverageExercisePrice" name="ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsassumedInReverseRecapitalizationInPeriodWeightedAverageExercisePrice" type="dtr-types:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_IssuanceOfPre-FundedWarrantValue" name="IssuanceOfPre-FundedWarrantValue" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="tpst_TrancheBTermLoanMember" name="TrancheBTermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_IndividualsWhoWereNotPreviouslyEmployeesOrDirectorsOfCompanyMember" name="IndividualsWhoWereNotPreviouslyEmployeesOrDirectorsOfCompanyMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_TrancheATermLoanMember" name="TrancheATermLoanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAssumedInReverseRecapitalizationInPeriod" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_AtTheMarketProgramMember" name="AtTheMarketProgramMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="tpst_ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumNumberOfSharesAvailableForGrantPerYear" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardMaximumNumberOfSharesAvailableForGrantPerYear" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="tpst_AccruedClinicalTrialLiability" name="AccruedClinicalTrialLiability" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="tpst_JefferiesLLCMember" name="JefferiesLLCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
</xsd:schema>
