No !!! You must use the thermal paste you have only if the thermal pad on heat sink is missed.
You may use a thermal paste only if you remove (i.e. using alcool) the thermal pad.
The theory which governs the heat transfer between the CPU die and the heat sink and then the ambient has been already exposed several time on this forum.
The CPU has, in some way, to disperse the heat it generates during operation. The power it can disperse is directly proportional to the difference between the CPU die temperature and the ambient temperature as well it is proportional to this difference by means of a coefficient which depends on the speed of air which lap the CPU. This last coefficient represent a resistances to the heat to be trnsfered to air. This resistance also is function of the ability of air to dissipate the heat. As an example, air has the lowest ability to dissipate heat, silver and copper has the best ability. The thermal paste or also the thermal pad are not so good as copper or silver but much better then air. The heat generated by the CPU is transferred to the heat sink through the thermal paste/pad which has the charge to avoid air to be enclosed between the CPU die and the heat sink.
Because the thermal paste/pad has a lower ability to transfer the heat with respect to copper, it is important to avoid a too thick layer of thermal compound between the CPU and the heat sink.
In this way the CPU will disperse the generated heat not through air but by means of the heat sink. The heat sink has an enormous heat exchanging surface with respect to the CPU die, resulting in a big reduction of the cpu temperature. Moreover the fan can increase the speed of the air lapping the cooler surface, even reducing the CPU temperature.
To have the lowest cpu temperature you should: use a copper heat sink, a good fan, use a good thermal paste (i.e. Arctic Silver 3), reduce the ambient temperature (cooling the case internal by air circulation).
The thermal paste (it is very soft) should be replaced ever 4÷6 months. The thermal pad generally does not need to be replaced, even if it has a little lower ability the transfer the heat.
______________________ <font color=red>A straight line never ends……………….until it comes up against a vicious circle</font color=red>