Also, pop the case open and have a look around the CPU and heatsink.
Depending on how long you have had the computer or where it is, you may have a build up of dust, which will cause higher than normal temperatures, possibly high enough for the computer to force a shutdown to protect the CPU.
Compressed air is great for removing the dust, however, make sure you stop the fan from spinning with something like a toothpick, as the jet of air may cause the fan to spin too fast, possibly damaging the motor.
I have found that 'canned air' is next to useless, so if you have a proper compressor out the back, use that.
Failing that, a selection of soft brushes are useful, along with some lung power.
You don't need to remove anything in order to clean the heatsink.
Also check the air intakes for dust, especially the PSU, last time I cleaned my computer I took a 'carpet' of dust off of mine.
