Hey,
I really wanted to play brink, and now that I am, it's really fun.
Problem is this game is literally killing my computer. Every 5-30 minutes the game makes my system restart itself (due to overheating, I guess), or sometimes even hard-freeze (I have to plug it out and back in to restart it).
I have played much more demanding games, but none of them crashed or hard-froze my PC.

My specs are:
Intel Core2Quad 6600 (2.4GHz x 4)
4GB DDR2 Ram
GeForce 460GTX (Overclocked right out of the box) 1GB
Windows 7 Home, fully updated
Latest nVidia drivers (Downloaded them yesterday)

I am aware that this might be a problem on my end, as my computer might not be able to cool itself properly, but I have never had a game hard-freeze my computer like this.
Can anyone suggest something I can try to do to fix this please? Thanks!

Start monitoring your temps. Find out what is overheating. Basic troubleshooting 101. Find the source of the problem before you try and find a solution.

try downing the ingame settings.