Cells on thermometers are in regions of strictly increasing size, starting from the bulb end (e.g. if the bulb is in a 2 region, the next cell along the thermo is in a region of at least 3 cells).
I've created an example puzzle and included its solution here as well.
Solve the example in Penpa+ (answer check enabled)
Solve the main puzzle in Penpa+ (answer check enabled)
Enjoy!
Solution code: Column 4, followed by Column 17 (no spaces).
on 31. March 2023, 20:12 by BenceJoful
Extremely nice puzzle in logic and appearance! I made a minor mistake toward the beginning but was able to salvage it after all :)
on 20. October 2022, 07:40 by Agent
Very nice puzzle! It looked impossible near the end... except for one specific way :-)
on 15. March 2022, 00:36 by MariaL
Excellent Fillomino PUZZLE!
on 13. March 2022, 09:34 by Crusader175
That ending was very tricky but very fun puzzle!
on 10. March 2022, 22:58 by SimplePurpleFrog
Beautiful and approachable logic. Loved it all the way.
on 7. March 2022, 15:02 by Vebby
Beautiful! Great fun to solve, especially the tricky ending. Thanks Pancake! :)
on 7. March 2022, 14:54 by grkles
I have very little experience with fillomino so I feel like I can't rate the difficulty, but I thought the logic was incredibly beautiful!
on 7. March 2022, 14:16 by au voleur!
Fun! I agree that it was easier than 4 stars, but it still had a nice variety of logic!
on 7. March 2022, 10:23 by MagnusJosefsson
Very nice and approachable Fillomino variant! Significantly easier than four stars in my personal opinion, so a good choice even if you are new to Fillomino.
on 7. March 2022, 05:46 by PulverizingPancake
Added example puzzle