is this a desktop or laptop?
If a desktop, it's most probably the fans, esp the one on top of the CPU and GPU (a black box on the motherboard, and the fan on the graphics card). If it is getting that bad it turns of, the build up is probably quite significant. You will need a mask (or breathe dust all you want), and small screw drivers to take the fans off to clean them. Make sure to be very careful when handling the circuit boards, esp the capacitors, if you are not gentle and knock them over, they do break.
If it is a laptop, basically the same thing. Most cases have screws that allow you to take most of the bottom off, you should unscrew the copper heatsink, there can be massive build-up behind the heat sink (where the 'radiator' of the laptop is). Last time I did it it wasn't dust, it was a film that I peeled off... =\