Kinematic convection models of the earth's thermal history are computed assuming that subducted slabs, along with some entrained material, sink all the way to the core-mantle boundary. The temperatures within the lithosphere and within the mantle away from sinking slabs are computed assuming that the return flow from the core-mantle boundary to the surface can be considered as slow, vertical advection. In the models, a drop in asthenospheric temperature occurs near the end of the Archean when subducted material first returns to the surface. This drop is about 200 ¿C if the subducted material does not mix thermally with the mantle on its way down and if only a thin thermal layer exists at the core-mantle boundary. We consider the possibility that this temperature drop is an explanation for the transition between Archean and Proterozoic tectonic styles. An implication of the kinematic scheme is that the asthenospheric temperature increases gradually during the Archean until the cooler material reaches the surface. After the Archean, the thermal evolution is similar to a well-mixed model. A difficulty with the convection scheme, as well as with any temperature profile in the mantle, which is basically adiabatic, is that excessively low temperatures in the core are implied. If a 100-km thick thermal boundary layer at the core-mantle boundary is included, then higher core temperatures occur, but there is a smaller drop in asthenospheric temperature at the end of the Archean.