I just built a new computer, it's an i7-930 with radeon 5870 in a micro ATX case. The computer started up and ran perfectly for the first day or so, including playing some games. However the first time I ran Crysis after like 20 min it suddenly shut down and resulted in a BSOD ("machine check exception). The way it shut down was it would exit to desktop and Windows 7 would start logging off and shutting down, not like a sudden power outage or something. The computer is able to restart with no problem, and runs normally until I play a game again. The only game I'm playing these days is Starcraft 2 and it happens during that too. I downloaded some temperature monitoring software, and it seems like the CPU temperature was at about 70-75 C when it happened. Also the last time it happened the game started stuttering and I would hear this noise, and then Windows would start shutting down like it did before. What's the likely problem here, and what should I do?
70-75 C is normal 'load' temperature for an Intel Core i7 series processor anyway, they are rated to run much higher. It won't experience stress until 80C or even 85C.
You might want to go into your BIOS and double check that it is not initiating a system shutdown on a low (75C or less) CPU temperature. (or other installed system tool that is paranoid about 70C being 'too hot' for a CPU or GPU - it's not).