No, you need just the core (if P4 & A64) covered because...lucifersam said:you dont just want the area where the core is covered it all needs to be covered to allow greater surface area for heat dissipation
Thermal grease's primary purpose in electronics is to mediate small surface imperfections between an integrated circuit (also known as a chip) and a heat sink. When applied in appropriate quantities, it fills the tiny pits and grooves — particularly on today's CPUs — thereby increasing the amount of surface-to-surface contact with the CPU die. Without thermal grease aiding the heat sink, CPU power dissipation overheating can occur and will generate logic errors as the heat raises electrical resistance on the multi-nanometer wide circuits.