FWIW, my PC had similar problems randomly about a year back. I started running a heat monitoring program because I felt that overheating was the culprit. I was surprised to find that it was not the CPU or GPU that was overheating but a chipset on the motherboard. I believe it was the northbridge or southbridge, I do not recall exactly which, I am certainly no expert.

That said I removed the chipset in question and found that it was very similar to the CPU and it used thermal paste...the problem was that the thermal past was virtually non-existent it had dried up or something. I cleaned it up, re-applied thermal paste, and put everything back together..I have not had any problems since.

A few different programs will monitor various different temperature readings and if you find one that is getting high you can look up what the reading is for. In my case the temp reading for the chipset was called TEMPIN1 or TEMPIN2 or something to that affect and with a little investigating I found exactly which point on the motherboard this referred to.