I yust installed Ubuntu 20.04 on my Surface Laptop 1 and I have Thermal Throttling issues.
You might not be the first
Well, Ubuntu Mate is still Ubuntu
Yes...but no.
When we're talking about the base OS (terminal/textmode stuff): yes, the base is the same.
When it comes down to the graphical part (GUI) : definitely not
Ubuntu makes use of the GNOME desktop: a not so efficient graphical interface + subsystem that eats resources for breakfast.
Ubuntu-MATE makes use of the MATE desktop which is fast, snappy, humble with CPU, GPU, RAM and battery and therefore overall a better OS for battery operated equipment (Laptops and tablets) or equipment with non-adequate cooling (for instance HP-laptops).
You really would have more chance on a solution here:
Ofcourse we would like to help you but since a very big and important part of your system is very different from ours, we might not have the best situation to come up with an adequate solution.