have you tested other components? I had relatively random crashes in lots of games in one of my kids' systems in the past 6 weeks. Everything seemed to suggest the video card was the problem given it would blue screen in almost all games within 2-5 minutes. I thought for a long time it was the card with an intermittent error. In the end, I went through piece by piece to check other components and found a badly seated memory stick was the problem - causing intermittent/random bsod's, especially under the load of gaming.
I'm not saying it's not your video card, but I'd run other tests first. Check CPU temp and shut-down threshold. Turn off auto-reboot and see if you get bsod codes that provide clues. Above all, get hold of a bootable MemTest and put it on a stick drive or CD and boot from it and let it run overnight. If the MemTest is clean and the other parts check out (temps, etc) then I would reasonably conclude it's the video card or a mobo problem.