Overheating of the CPU is still possible.
Overheating of the GPU is still possible.
Bad power supply is still possible.
Bad RAM is still possible.
Bad CPU is still possible.
Bad Motherboard is still possible.
If I were to guess, I would say the most likely culprits are RAM, Power supply.
Bad ram will cause your system to hiccup and even BSOD or freeze up every time a bad place in memory is used to store something.
A bad power supply can short power your CPU causing it to shut itself off, effectively freezing your system.
I have a system that does something similar to yours, if I just leave it on, randomly I will come back to it and it's off, other times it has lasted weeks. Sometimes if I run a game on it, it will just shut down while I am using it. It is most likely the motherboard (The mobo has been replaced 3 times already in that machine) or the power supply, or both (Bad PSU could be damaging the boards).
I had another system that often froze up or crashed stuff (Especially web browsers). Turns out it was cause the Mobo was broken and it was stuck with a BIOS firmware that didn't understand the processor and wasn't giving it enough power. All BIOS flashing failed on it, so bad board. Took a long time to figure that out. (Its a funny story actually, but Linux people will hate the story).
On the same system, a few years later, the PSU apparently started to get weak, and started blowing up my video cards. When a video card goes, usually your system refuses to boot and just keeps restarting, or it will magically shutdown and reboot while your using it (Reminds me of a hellish time of my life involving iMacs).
So, can you please run a program like SpeedFan, and tell us the temperatures in your system. if you can, try and watch it while playing a game. Ideally a CPU should never exceed 70C, a GPU should never Exceed 80C. Most GPU's go critical at around 90C-120C
We can also use SpeedFan to monitor the voltages from your power supply. If your temperatures check out fine, then we will check the voltages next.
Direct Download
http://www.almico.com/speedfan439.exe
Website
http://www.almico.com/sfdownload.php