|Yes, but you won't get much dust off of the fans as they aren't usually located anywhere near a fan not to mention for the most part they are enclosed and will not let much air through them to the inside of the case.|
It sounds like your computer is randomly shutting down and you may think it is a heat related issue? If this is the case, do you have a desktop computer or a laptop? Do you see a blue screen or any type of error message before the computer turns off? Do you notice it shuts down while you're doing something that may be taxing on the CPU or does it just shut down shortly after startup?
Sorry for all of the questions, but there are several things that could be causing your computer to shutdown.