This sounds exactly like a power supply problem I had a while back. The PSU would reset after it was unplugged for a few minutes, then no problem until the next random shutdown. I thought mine was heat related as well, but it just turned out to be a crappy PSU. Replaced it and never had another problem with random shutdowns.
As I get older, I'm starting to think computers are more magic than anything else. Any crash can be caused by anything. For example, running Folding while doing something 3D will crash my computer, but Folding alone or gaming alone will not. Solution? Increase the CPU voltage. Seriously. This actually worked. My computer doesn't crash anymore.
Regardless of how to fix the problem, you can start searching for the problem:
-Run OCCT small units to test the CPU alone. IMO, this causes the fastest CPU failure. I love OCCT because it makes a weird quacking noise on failure
-If that passed, run OCCT Linpack 90% memory to test overall CPU/mobo/ram. I've never actually seen Linpack fail at something that is OCCT or Prime stable, but others claim it can. This is probably because my northbridge, memory, and HT are always underclocked slightly.
-If that passed, run the OCCT GPU test to test the video card's processors.
-OCCT's video memory test doesn't work on AMD cards, so for those I use Furmark. Test the video card memory by setting Furmark to at high resolution, full screen, with the highest antialiasing. If your video card is screwed, this will crash almost immediately by the screen artifacting then crashing to blue screen. If it crashes to a black screen, it's a PSU failure.
-If all of those passed, run the OCCT PSU test. This will crash to a black screen if the PSU sucks.
Even when the tests complete successfully, look at the voltage graphs OCCT saves. A good PSU will show sharp, right angle voltage changes. A really screwed up PSU will show wavy voltage changes, almost like the PSU is saying "yeah I'll change the voltage, just hold on a minute."
Like I said in the first paragraph, try repeating the tests while Folding GPU is running. It seems like Folding and gaming use two completely different parts of the video card.