My friend's computer is freezing. Is it the processor?

I recently sold my friend my old computer. Right after he got it, it started to freeze and shut down without any error messages or anything. The screen went froze and got a little glitchy, and then the computer just shut off. This was familiar to me because I had the same problem just a few months earlier, which I fixed with a simple cleaning. The motherboard told me that the processor was overheating.

Now I wasn't able to disable the BIOS message that said the processor was overheated, so when I sold it to him it had that error message. So we aren't certain that the processor is the problem, but we are pretty sure.

Since I figured there might of been a problem with the thermal grease due to the cleaning and fooling around near the heatsink and cpu, he managed to change that. Since, the computer was able to run a day or so, but recently it just had the same problem of overheating and shutting down, even with all the attempts to clean and switch things.

Unfortunately this is the only information I currently have available. Is there any way to cool the processor down? Or is a setting off in the BIOS were it does an emergency shutoff at a much cooler temperature than needed? Or is it even the processor at all? Please help!