I have no idea... but are you comparing the same releases? (or really same kernel stacks?)
I was QA-testing a jammy ISO on a box yesterday, and it appeared to cause the fan to run more that I expected (the device was running hot so fan on was expected; but hotter than I expected), using way more power too, but I doubt it's any changes other than possibly later kernel. I ignored the issue, if it continues to occur - I may explore it, but for now it's just subjective feeling.
But are you comparing a Ubuntu with GNOME and the the Ubuntu MATE using the same stack? or a different kernel stack?
(You didn't provide release details; so were the same release? or different releases? If using a LTS release; two kernel stack choices exist - with 20.04 the GA kernel is 5.4, or with HWE it changes over the life of the release (so two 20.04 systems may be using different kernel stacks). If using a LTS release, you can switch the stack you're using which may help/solve the issue as it's not a MATE vs GNOME issue. Use uname -r
to see what kernel you're using. I could be way off here sorry; my thoughts colored by the QA-test yesterday which I didn't explore just assuming it was kernel stack differences for me)