The P4 processor came with a heatsink/cooling fan that had a compound on the fan unit. It seems like I read somewhere that you can use a silver thermal compound or the supplied compound on the fan but not both.
The fan that comes with the Processor is not the greatest cooling fan. but you can use the thermal paste that is found on the fan.
I scraped it off and used my own thermal paste. (I applied it on the CPU so you don't put too much on plus you know it is covered.)
I have never heard of using both... using too much is not a good thing!!! use one or the other.
the paste is designed to make sure there is no air gas between the CPU & heatsink plus it helps facilitate the transfer of heat from CPU to heatsink.