wipe away the thermal paste that came with the stock cooler its crap. then apply new thermal paste to the cpu not the cooler! do not use to much. there are different ways of applying it. some say make a "X" in the center of the cpu others find that a "dot" in the center of the cpu is best and let the preassure of the cooler spread it evenly. either way is good just don't use to much or to little.
The CPU should work fine with the material on the stock cooler, but it may run a little hotter than with a better grade of paste. Just be sure to follow Ferny's advice and remove the stock stuff completely if you're going to apply something else.