A little bit of a laundry list of things to try:

Have you measured the power supply voltages? Only do this if you are comfortable. If so, check them when it's been off (and works), then let it heat up/act up, then recheck the same supplies for a change in voltage. What do you have for meter?

If it heat's related, get a can of freeze spray. The upside down aerosol can trick mentioned above works to an extent. Freeze spray will definitely take it well below sub zero. Hit or miss since you are sort of guessing when the problem area is at.

I don't think you replaced the battery? I don't know if that's an issue or not, but it's so simple I'd do it anyway.