Uh... better check out some instructions using thermal paste (like this one:
http://www.arcticsilver.com/arctic_silver_instructions.htm). If you remove heatsink (for checking or any other reason) after applying paste, you should wipe both clean from paste beofore applying new one.
Personally I used is some Arctic Silver 5 with my CSPPC, but that stuff of yours is probably enough.
Btw., that small piece of metal is in fact the cpu-core.