This desk top PC with Windows 7 has unexpectedly shut down on several occasions without sign of a power surge. It has REBOOTED alright. I suspect it shut down due to overheating because of accumulation of dust. If this is so, what should I do to eliminate the problem?Clean out the dust.
And check to SEE if all fans are turning.Does that mean I have to take the top off or can I check the fan from outside. I also understand that I should not use a vacuum cleaners as the static could cause problems in the computer systems.Get several cans of compressed air and use those.  Yes to best clean they system you will need to remove the system lid.  Do NOT turn the cans upside down always use them face up.  Clean the machine in a well VENTILATED area (outside).  Hold the fans still to prevent them from spinning.

DO NOT remove the heat sinks just blow the dust off of them.  Blow the power supply out as well.

Unplug the system and GROUND yourself to prevent a static DISCHARGE from you that can even brick they system.Thanks for that advice Rustys.