What would cause an old desktop PC to keep rebooting its self?

I would suspect your cpu is overheating, but it could be because of inadequate cooling in your case, or your cooling fan on the cpu itself if getting clogged with dust, and the fins on the cpu heat sink getting clogged up, not allowing the cooling it needs. If the cpu fan slows down and can't keep up, you might need a new fan.

Also, on hot days, the air coming into the case may not cool as it should, and if the case fan (s) cannot keep up, the whole system suffers. 10 degrees hotter case is also 10 degrees hotter cpu and the cpu fan has to use the hotter air to try to cool down the cpu.

So make sure you have a dust free case, a good case cooling fan set up, and your cpu heat sink is not clogged, along with your cpu fan being up to the job.

Adding other devices such as extra hard drives and cd dvd drives, also adds heat. Video cards add heat, and the power system should have its own heat fan, but can be a source for extra heat.

Download and install Speedfan (free) and set it up to check your temps of your cpu, hard drive video card, etc.,

Hope this helps.

Your processor, its probably that. My computer turn itself off whenever it gets too hot. Sometimes it might be a virus or your computer just cant handle some program. Theres a virus which keep you in a reboot loop.

Check for dust on CPU and in power supply.