More than likely the A/C is coming on because there is high humidity. The HVAC control module wants to remove this moisture from the air so that when it is blowing it doesn't fog the windows and has a better ability to defrost the windows. If you are blowing moist air onto a cold window it is going to fog or frost so it is try to control this humidity and it can only do that by running the compressor.
As for this noise and heat issue, this sounds like blend door issue but it would really help if you could get a video of this noise so that we can get a better idea on what needs to be done.
Here are some guides that have some good info in them but hearing this noise will tell us if we are on the right track:
Saturday, February 20th, 2021 AT 4:10 PM