Sounds like a cooling issue as in, it ain't getting enough cooling. Seriously, games tend to demand more of your hardware and generate more heat.
Monitor your temperature before you play a game. Fire up a game and play it for 10 or 20 minutes (however long you know you can safely play before crashing). Alt+Tab out (or quit the game) and immediately check temperatures (video card, motherboard, CPU, ambient, etc.).
No matter the results, open the case and blow everything off, get lots of air flowing in there (I have even used house fans at times when dealing with cooling/heat issues).
Hope you get the problem solved.
