Les, even if the fan is moving air, the heat sink on the chip may be clogged with dust, impairing its' ability to radiate heat. Not unlike your refrigerator coils getting dirty.
Heat sinks, power supply(ies), fans, air vents, all must be cleaned. You will likely find that your computer will run at much higher indoor air temps when this is done.
One of my customers used to take computers into the repair bay to blow out the dust with air from the shop compressor. Don't do that. Shop compressor air may have water, oil and other contaminants in it that won't hurt the impact wrench but does bad, bad things to your computer. They didn't believe me and ended up learning this lesson the expensive way.
Use a paperclip or some other object to carefully prevent fans from spinning on a shut-down and unplugged computer when the air might spin them. Some fan bearings will break if you spin the fan the wrong way too fast or too long.
If you want to dust the insides, pull the power cord after shutting down the PC. Sometimes there is a constant power pull and using canned air can short the motherboard.
Without a doubt unplugging it (and removing the battery, if it's a laptop) is good advice before opening it, every single time. I used to have the kids that worked for me put the power plug in their pocket to keep end-users from plugging stuff back in while they were working on them. However, I've never heard of canned air by itself causing problems.