Ok, I've tried improving the air flow, but still no luck. I've also tried formatting and reinstalling everything to see if that helped, but that didn't work either.
My temperatures should be ok according to what I've read, so I'm really confused about what the problem could be.
Can the GPU cause games to just crash like this? Or would something else happen in that case, like graphical glitches or something?
If the CPU is the problem, what signs should I look for? Could it be the motherboard?
EDIT: Starcraft 2 runs like a charm even on the highest settings, even in multiplayer. I also tried moving Battlefield 3 to my SSD drive, so I don't think the HDD is broken.