Most convection studies of thermal history have not considered explicitly the thermal interaction between the mantle flow and the core. We have investigated the influences of variable thermal conductivity and variable viscosity (temperature- and pressure-dependent) on the boundary layer and thermal characteristics of the D″ layer, and the evolution of the thermo-mechanical profiles of horizontally averaged viscosity and thermal conductivity. Viscosity contrast due to temperature dependence of up to 30,000 has been considered. Our results show clearly that variable thermal conductivity, though small in magnitude as compared to variations in the viscosity, does exert a significant delaying influence on mantle cooling, thereby keeping the Urey ratio low, reducing the growth of the bottom thermal boundary layer, and changing the viscosity profiles over time. A higher temperature at the core-mantle boundary increases the overall time-dependent behavior of the thermal boundary layers. Enhanced radiative conductivity results in faster cooling, opposite to the effect of the phonon conductivity component and a superadiabatic temperature gradient in the deep lower mantle. Finally, the initial value of the core-mantle boundary temperature can be inferred to wield a strong influence on the subsequent mantle thermal evolution in this model with both variable thermal conductivity and viscosity. We may conjecture that other rheological and conductivity complexities, such as grain-size dependence of mantle properties, would also have an impact on the current state of the mantle resulting from the primordial thermal condition.