Your temp difference is a bit odd man. You should really make sure you wipe it all of and reapply evenly when you get a new heatsink. Mine will be no more then 2c off from the other core.
I recently had a lot of trouble with my computer over-heating. I found a great article entitled "PC Heat Stroke: What to do when your computer overheats" at http://www.itinfoonline.com.
I ended up needing to install a new PSU (fan died).