Hello JorisIn,
The problem is not the video card from the looks of it.
It sounds like you have an overheating problem, If you want, download cputemp and post the readings as a reply and i would be glad to help. Minor checkings, have you tried to see if the gpu fan is spinning? It may also be getting hot. Cpu cooler? If nothing gets ressolved, you'll have to replace the thermal paste and see what happens from there.