Thermal paste is used ONLY BETWEEN a heated device and a heatsink that carries heat away from the device to some other means (like air blown by a fan) of removing the heat. It enhances the rate of heat flow from device to heatsink.
For any HDD the means of removing heat is AIR FLOW over the outer case surface of the unit. Merely covering that case with thermal paste actually would apply an INSULATING layer and make things worse! ADDING some kind of finned heatsink to the HDD would require using a THIN layer of thermal paste between them AND finding a way to ensure the two units are VERY tightly connected. NOTE that, when using this technology on a CPU, the CPU case AND the heatsink contact surfaces are VERY FLAT and polished BARE METAL so that they can make efficient contact for heat transfer. The outer surface of an HDD is PAINTED and that alone is another layer of insulation to interfere! Additionally, the HDD case is FLEXIBLE enough that you can NOT ensure it will remain flat in good contact with another surface.
Don't try this!