Box 1 has some interesting restrictions because of some low numbers:
A 6-thermo can only be 1-5:[234] or 2-4:[13], so cells are [12]:[54]:[1234]
However, a 1 in column 3 would start a thermo downwards, as would a 2, as that can only be prevented by a 1 below it, but 1's taken. So the cells are [12]:[54]:[34]
An 11-thermo staring [12] can only be continue [2349], but again 2 can be excluded due to there being no row two thermo.
A 10-thermo starting [45] can only be 4-6-low.
4,6,2,3,1,5, and 9 all place themselves in box 1, leaving a [78] pair.

Box 3 also has some restrictions based on low numbers:
An 8-thermo and can begin [123], but 2 and 3 are excluded, so r1c9 is 1.
The 9-thermo cannot be 1-2-6 or 1-3-5, so is 1-8.
The 8-thermo cannot be 1-2-5 for several reasons, so is 1-3-4:[2] or 1-7:[llow]
Given that an 8 in row 2 would form a thermo from any number other than 9 in row 1 of box 2, we know that there is a 9 there, and that it shadows the 8.
This places the 9 in box 3 in row 3.
The 11-thermo in box 3 cannot be 1 cell, or 3, or stop after 2 if the 2nd one isn't a 9, therefore it's 2-9:[low].
This excludes 1-3-4 as the 8-thermo, so 7 goes in 2rc9

Column 9 now has some restrictions based on high digits:
The 9 will have no thermo, and the 8 could only form a thermo with a 9 behind it in column 8, but that's excluded. Therefore two [89] pairs can be placed in column 9.

Box 3 is now starting to be constrained more heavily:
The 15-thermo upwards immediately stops at the [89], and can't have a 7 on it, so is 6-9, resolving the 8 too.

The 23-thermo in column 8 is very restricted - it can't include the 9 in row 3 as its endpoint, and therefore it is 5 cells long.
The top 4 cells 8-[345]-9-[?] must sum to 22 by magic, so [345]+[?]=5. 5 is excluded, and ? is now [12].
The thermo must therefore contain 7, 6, and 5 at its top, and a sum to 5 at its bottom.
The 10-thermo in box 6 can now only be 4-6:[low]
3 and 5 now complete column 9, which resolves other cells in column 8 and nearby
The 21-thermo in row 5 must end with a 9.
The 23-thermo in row 7 still needs 15 more, and can't end -6-9, so must be -7-8.

Row 9 now has some restrictions based on availability of low numbers.
A 7-thermo that can't start with a 1, or have a 4 in the second cell is a 2-5:[134]
The 9 must be in one of the columns without a thermo, column 4 or 6.
The 7 can only be extended into a 15, 16, or 24, but those thermos don't exist, so the non-thermo edge cells in box 8 are a [79] pair.

We're now well equipt to tackle box 7:
Sudoku places the 3 in r9c2, and leaves a [45] pair in row 9.
The 11-thermo in column 1 may only be 4-7, or 5-6.
The 12-thermo in column 3 similarly is 4-8, or 5-7.
The 21-thermo in row 8 must contain at least 3, and at most 3, cells between 6 and 8, so is 6-7-8.
This puts a [13] pair in box 8, and lets the 4 and 6 be placed uniquely.
The 19-thermo still needs 9, and sudoku places the 1 and 2.

Box now has lots of openings:
The 11-thermo can only be 3-8.
The 4 and 7 place in column 1.
The 1 and 2 place in column 2.
The 5, 6, and 9 place in column 3, remembering that the 11-thermo in row 6 must not be extended, so the 9 can't go there.

Now it's mostly sudoku:
Column 5 has a naked 8, 7, then 6.
The non-existence of thermos in box 2 means that an edge 9 must obsure the 8.
r6c5 is a naked 7.
Finally, the explicitly marked 2-cell thermo kicks in, it needs to go from [29] up to [13], and therefore is 2-3.
Everything else just drops out after that.