Computer shuts down after some minutes

[Googolplex]

I finally did a CPU stress test with Prime95 and let my CPU burn 10 minutes over 96°C. The computer was not turning off. So, I think, it is not a CPU problem! Notice I'm just using a cheap cooler like the intel stock. But the CPU seems to be stable at 96°C.

In normal windows running, the temperature is about 65°C @ 2,17 GHz (underclocked).

But why my computer is turning off when I play a game?

I'm sure, it's also not the graphics card. I had the same problem with my old GeForce GTX 275, as I bought a new GTX 560 Ti, the problem still appears. It must be the power supply, or?

My power supply is a 550W BeQuiet!
Normally it sould be a good quality, but what could cause the problem?

When I buy a new PC, I'll also buy the Arctic Cooling MX-4 paste.
But I can't understand why my PC always turns off when gaming.