Certain computer games shut down my computer

First off, I'd like to say that this isn't an overheating issue, because I am able to play Computer intensive games (like Star Craft II) for 4+ hours with no problems, but I can't play certain games for longer than 15-20 minutes. So far it has only happened to me with 3 games:

1. Halo Combat Evolved
2. Assassin's Creed II
3. Brink

If it was only Halo, which is an older game, my guess would be that it is a driver/compatibility issue. But when it happened with Assassin's Creed II and Brink, it totally baffled me as to what could be the problem. Before they shut down, They usually freeze for a second and then the screen goes black and then shuts down(without restart). Brink had the odd case of having it go a bit laggy, and the textures being blurry(not loaded properly) and then freezing>shutdown.

It is really bugging me as to what the problem could be, because its making me feel insecure as to whether I should get other games, because I'm afraid my laptop will turn off, and I won't be able to play it properly .

Oh I'd also like to say that after a shutdown, CS : S gets very buggy for a bit, and then returns to normal, I haven't noticed it on any other games happening though...

Any Ideas?
Thanks in advance!

I have checked using multiple programs (deFraggler, and speccy) and the temperature of the laptop does not go more than any of the other games. I have also compared how hot my laptop is when I am playing games, and again, there is no noticeable difference from Starcraft 2, or Counter Strike or Brink or AC2. Overheating was my first guess too, and that was the first thing I looked into, and I'm very certain that that is not the issue here :\

I would also like to mention that Halo and AC2 have shut down before my computer has had a chance to get near potential overheating.

Alright I'll try that when I get home. It doesn't really explain Halo though, as it has very low PC requirements.

I tried AC2 with lowest settings yet it still shutdown.. Any Ideas?