Thermal paste helps facilitate the transfer of heat from a processor to a heat sink. Without thermal paste heat will remain in the CPU and overheating will occur.
Wikipedia
Thermal paste (also called thermal compound, thermal grease, thermal interface material (TIM), thermal gel, heat paste, heat sink compound, heat sink paste or CPU grease) is a thermally conductive (but usually electrically insulating) chemical compound, which is commonly used as an interface between heat sinks and heat sources such as high-power semiconductor devices The main role of thermal paste is to eliminate air gaps or spaces (which act as thermal insulation) from the interface area in order to maximize heat transfer and dissipation Thermal paste is an example of a thermal interface material As opposed to thermal adhesive, thermal paste does not add mechanical strength to the bond between heat source and heat sink