Cobwebs, schmobwebs....
Two things are important. Airflow and heatsink conduction. Everything else is just cosmetic. If you've ever done computer work for a smoker, you know that fanned heatsinks accumulate tar between the grills. This insulates the metal and keeps it from operating more effectively.
So, like I said. Buy that heatsink a drink of alcohol. Propanol (iso-propyl 90%+) that is. Use a pipecleaner or pulled Q-tip to get between the grills. If you wan't to remove the CPU heatsink, have some thermal paste (Arctic silver preferably) around to re-apply.
Bottoms up homey!