Absolutely...depending on the actual situation/is the pc on the floor or on a desk, are there pets like cats or bunnies around etc the dust build up can be too much in as little as 6 months
The more dust build up you have, the less effective is your cooling thus the cpu gets hotter and eventually shuts down (or worse gets destroyed in the process)
I usually just use canned air and a stiff paintbrush/old toothbrush to remove dust from the fan blades and the heatsink "griddle" but in extreme cases I take off the heatsink, clean it out, apply new thermal compound and be good to go for another 6-8 months
-DG
The working for short times but the crashing over longer periods is as good as a dead giveaway