Operating lease commencement month and year.

No definition available.

Name:	tpst_OperatingLeaseCommencementMonthAndYear
Namespace Prefix:	tpst_
Data Type:	xbrli:gYearMonthItemType
Balance Type:	na
Period Type:	duration

- Definition

Area of a real estate property.

+ References

No definition available.

+ Details

Name:	us-gaap_AreaOfRealEstateProperty
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:areaItemType
Balance Type:	na
Period Type:	instant

- Definition

Term of lessee's operating lease, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
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-Section 50
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+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Definition

Maximum borrowing capacity under the credit facility without consideration of any current restrictions on the amount that could be borrowed or the amounts currently outstanding under the facility.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
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+ Details

Name:	us-gaap_LineOfCreditFacilityMaximumBorrowingCapacity
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
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+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of operating lease expense. Excludes sublease income.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 4
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+ Details

Name:	us-gaap_OperatingLeaseExpense
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
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+ Details

Name:	us-gaap_OperatingLeaseLiability
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of lessee's right to use underlying asset under operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Subparagraph (a)
-Publisher FASB
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+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_CreditFacilityAxis=us-gaap_LetterOfCreditMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_StatementGeographicalAxis=tpst_BrisbaneCaliforniaMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Commitments and Contingencies - Narrative (Details) $ in Thousands	1 Months Ended	3 Months Ended		6 Months Ended
	Jan. 31, 2022 USD ($) ft²	Jun. 30, 2025 USD ($)	Jun. 30, 2024 USD ($)	Jun. 30, 2025 USD ($)	Jun. 30, 2024 USD ($)	Dec. 31, 2024 USD ($)
Loss Contingencies [Line Items]
Operating lease right-of-use assets		$ 8,104		$ 8,104		$ 8,643
Letter of Credit
Loss Contingencies [Line Items]
Borrowing capacity	$ 388
Brisbane, California
Loss Contingencies [Line Items]
Term of contract	8 years
Area of property (in sqft) \| ft²	20,116
Operating lease commencement month and year	2022-12
Operating lease right-of-use assets		8,104		8,104		8,643
Present value of operating lease obligations		8,663		8,663		$ 9,011
Rent expense		$ 486	$ 587	$ 973	$ 1,272