Computer shuts down after some minutes

[plutomaniac]

To format the hard drive surely isn't the issue.

That's correct, also check my reply above.

EDIT: The reason it shuts down now is because now the weather is warmer (unless you live in the north pole or something) and the cpu is getting even hotter. During the winter, even under gaming, maybe you were getting away with 85°C which is not normal but still...operational.

EDIT 2: Alright fine, don't buy any cooler or something. You could remove the cooler all the way, clean the cpu and heatsink from old thermal paste, apply new one, connect the fan and try again. That's my recommendation. Otherwise, I suggest you take it to a "professional" who will do the same steps.