Re: lets see your...
I used the thermal paste that came with my biggest Zalman CPU cooler thats now in ma g/f's case.
Personally i haven's done much research on thermal paste since i expect a aftermarket
CPU cooler brand woulden't put sh!t thermal paste with it lol.
I know there's better ones out there tho but i'd suggest to look up a review on whats best.
From what i read you allready had the CPU block off?
Higher temp in one core might be because of many reasons.
But yeah whiping the paste to the side by dropping it on the CPU might create a "hill" of thermal paste,
lifting the block off the CPU and so making it hotter since it doesnt get cooler properly.
Refitting is recommended then imo.