If it's a stock cooler then possibly. If it's installed incorrectly then it could most certainly be the cause of the overheating.
What kind of thermal paste do you have? I would recommend buying some Tunix Tx-2
from Newegg It's only 6 dollars shipping included.
It works much better than the white stock stuff. It's also arguably better than Arctic Silver, and it's non-conductive (unlike Arctic Silver) so, if you screw up you don't have to worry as much.
Also, make sure to THOROUGHLY clean the original paste from the heatsink base and the heatspreader on the processor. I usually use a lint free cloth for really gunky stuff, and scrub it softly with acetone, or isopropyl alcohol. Make sure that even the tiniest remnants are completely removed, because any gap between the Heatsink/CPU will cause a big rise in temps.
Apply a small pea sized dab in the middle, or better yet, check out Slaymate's Method
Be careful, and good luck.