It sounds like your motherboard has some microscopic broken metal traces on it. When you heat the motherboard with the Hair Dryer it causes the metallic traces to expand and make contact thus everything starts working normally.
Could also be that hardware is not making good contact with the motherboard and when you heat the motherboard the contacts expand making good contact again with the hardware.
Could also be some electronic part on the motherboard that is going bad and the heat makes it start working.
either way I would try another motherboard and see if the same thing happens.
But I just reread your original post and you mentioned this has happened with other motherboards. That pretty much eliminate all of the above that i mentioned.
So it could be a bad PSU.
I would use OCCT to stress test the PSU and see what happens. If it crashes immediately or what. Also check the PSU outputs and hardware temperatures and fan speeds to make sure it isn't overheating and your have proper 3.3/5.0/12.0 VDC output.