My comp keeps overheating and shutting down, what can I do?

Have you checked the fan is working? Is your PC over clocked? If it’s over clocked you probably need to take it to Geek Squad as it’s over fried!

Just had this problem with a Toshiba Satellite laptop. We took it apart and found a huge dust clod stuck right in the CPU fan. The dust clod was literally impairing the motion of the fan so that the CPU was overheating and automatically shutting down. After extraction with tweezers and a good cleaning with compressed air, the laptop's working well again.

Is this a desktop or laptop you're working with?

Gaming, HD Video, Large Software like video editing etc., consume more Processor resources and due to the heavy processing the system heats up. Excessive heatup beyond usual is alarming and PC shuts down by itself when the processor/ CPU temperature exceeds the safe temperature limit. There are mainly two reasons for heatup.

Heating issue generally occurs due to fan failure, which may damage the system, if not checked properly. Another most likely cause of overheating is the dust present inside the PC, which clogs the fan and heatsink.

• Make sure the fan is running. (if not, it needs replacement)
  
• Clean the fan and heat sink (thermal module). Take out the fan and heat sink and clean them with the help of tooth brush and put it back. Don't remove the heatsink if you think that it is properly placed and fixed in its place because if you remove it, you have to apply thermal paste on the processor to put it back.
  
• Also, make sure that the PC is placed in a well ventilated environment and the air flow the the PC is correct. You may consider adding additional Chassis Fan for better cooling.

The procedure is very simple and I believe immediate action is required to prevent any damage to your machine and data.
Source: Fixya

If you have not been playing with the internals... Then the most probable cause would be the processor fan, presuming this is not a laptop.

There is usually a small dedicated fan just for the processor which is in turn protected by a thermal shutoff.

As in: fan quits, processor overheats, thermal protection shuts everything down, thermal cools down, repeat ....