Anything running the Gnome desktop will work fine.
I also had a Surface Pro 3 running Debian + Gnome. I Gifted it to my father for casual web browsing and It's working great for him.
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Just this weekend I took an old Gen 1 Surface Go and put the latest Fedora on it and it's amazing, very intuitive for touch screens. Tried Mint before and it gave me enough issues that I didn't use that Tablet at all for almost a year.
Edit to clarify, I run Mint on my desktop and love it, just didn't really work well on my old Surface Go.
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Should try the surface Linux project. It is great and make surface usable fully on touch screen.
There are thermale configuration available too in their git.
Be aware their is a current bug in the touch system you have to ever write the default values. Here the issue which contain a solution https://github.com/linux-surface/iptsd/issues/171#issuecomment-2359625900
While you wait for responses, there is a lot of coverage on this already. Just search:
surface pro 3 linux
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