The effects of thermal coupling of the core and mantle on the thermal evolution and mantle dynamics of terrestrial planets are investigated using three-dimensional thermal convection models in a spherical shell. Three pairs of models are presented to study mantle models of different viscosities and internal heating. In each pair, one model adopts a constant temperature at the core-mantle boundary, and the other allows the core to thermally couple to the mantle and cool. In the first and second parts, the mantle is heated only from below, whereas in the third pair, internal heating is due to radioactive elements. The mantle viscosity of the first and third pairs is 1021 Pa s, while the mantle of the second pair has a viscosity of 1022 Pa s. The thermal coupling of the core and mantle has strong effects on the thermal boundary layer near the core-mantle boundary but only minor effects on the thermal boundary layer near the surface. It cools the core, substantially weakens the thermal boundary layer near the core-mantle boundary, and thus reduces the vigor of convection in the mantle. The models with cooling cores result in a substantially colder and relatively less dynamic mantle than the models with a fixed temperature at the core-mantle boundary which overestimates temperatures in the mantle. ¿ American Geophysical Union 1994