If you hear it engage, I suspect the problem is in the vehicle. Under the dash, driver's side. Near the center, you will see the HVAC box. There are cables that go to it from the control panel.
One of the cables is responsible for the air temperature that enters the vehicle. I have a feeling the cable is broken, out of adjustment, or disconnected.
I attached a pic below so you can see the item to look for. It's not a great pic, but you should be able to find it. Check the cable I highlighted. Change the requested temperature between hot and cold to make sure it moved the air mix damper lever. If it doesn't or if it is hardly moving, check for a possible reason.
Let me know what you find or if you have other questions.
See pic below.
Saturday, August 6th, 2022 AT 1:58 PM