More likely than not, it is a hardware issue. Software is never out of the question, though.
I had a similar problem happen while in the middle of a game - the thin metal on my stock AMD heatsink actually warped under the heat of my processor and fell on my GPU. My FPS plummeted from 60 to ~1, and opening the start menu to boot down took hours. I ended up just pulling the plug to prevent further damage.
Once you are near the computer, make sure you check every detail of the build. Then, with the side panel open, turn your computer on and if you smell anything burning, turn it off immediately and recheck. If nothing is burning, run some heat tests. If everything looks alright, and you still smell nothing burning, run malware tests.
I recommend Avast! and Malwarebytes.
1. I'd assume he'd be smart enough to do a visual inspection first.
2. If it is really the processor, one more boot isn't going to kill it.
3. If it's the heat sink missing, I'd be pretty surprised that it isn't shutting down due to heat. That's usually the big indicator of a heat problem.
1 + 2 are absolutely true. It wasn't meant as an insult to you, I was just making sure OP didn't make any mistakes that cost him his computer.
About #3, though, you'd be really, really surprised. Of course it depends a lot on the system hardware and varies from system-to-system, a friend of mine actually ran a computer of his for something stupid like 20 minutes until he smelled that his processor was hot. Then again, he had the heatsink on; the fan was just off.