It would be best to open it up and clean it out, but if you won't do that, a sort-of fix is to get a cooling pad with a fan to put your laptop on.
Something like this will work - http://www.amazon.com/Cooler-Master-NotePal-Cooling-R9-NBC-4WAK-GP/dp/B002MU1ZRS/ref=pd_sim_pc_8
The dust problem will just continue to get worse though. You should probably figure out how to open up your laptop.