Specific Heat Index describes how much heat (energy) is required per unit mass to change the temperature of something by a unit temperature. It takes more heat to change the temperature of water than to change the temperature of aluminum for example. I don't know the trends of different base oils for this parameter.
The higher the Heat Index, the more heat a fluid can carry away.
The ability to conduct heat affects how fast a fluid can absorb heat. The higher the heat conductivity(at a fixed flow rate), the faster a fluid will absorb heat until equilibrium is reached. Aluminum is a better conductor of heat than styrofoam for example. I think that polar fluids tend to win-out for this parameter.
Thermal stability describes the ability of a material to tolerate higher temperatures without degrading or reacting with oxygen. In this parameter, Group III, PAO, and esters beat Groups I and II.
The viscosity determines how much fluid can flow through the engine only when the circuit is in bypass mode. Low viscosity fluids will cool better because they flow better without building pressure.
I do not know what "thermal capacity" means as it is used in bepperb's post above.
So, if your pump is in bypass mode often, low viscosity fluid will cool faster. High viscosity will produce heat from internal friction (as stated by others above). However, without knowing the conductivity of heat and the heat index, I don't think that this question can be answered. I guess that some of the formulators will know the relative values for different formulations.