I remember reading somewhere that if your computer is set so that it will automatically shut down if it goes over your RAM's threshold, it will do so. My computer on its own will be fine, but as soon as I start playing a game (Diablo 3, Deus Ex: Human Revolution), it'll be totally fine, receive a few frame rate drops, and then shut down entirely.
Since my CPU is hardly working hard, and the rest of my computer is stuck ~40 degrees, I'm assuming it's that RAM problem I was reading about. So how do I stop the auto-shut down function?
Actually, could it have something to do with my GPU? When I plug it into my LCD TV (and set it to a resolution high than what is recommended), it'll shut down eventually, but plugging it into my old monitor will make it fine.
Could it have something to do with the GPU, then, and not the RAM?
I have no clue where you read that, but it doesn't make much sense and I never heard of such a configuration parameter. Check your video card's temperature while using a tool like Furmark. You can also use Prime95 to test the CPU and make sure that it doesn't overheat while being 100% busy for several minutes (or hours for a really good test).