Recent geochemical and isotopic data support the hypothesis that the earth's mantle convects in two separate layers with an interface at the 650-km seismic discontinuity. This paper studies the implications of this hypothesis with regard to the thermal boundary layers that are expected to develop adjacent to the interface between the convecting layers. We are particularly concerned with a possible decrease in the mantle viscosity across this interface. In order to study the structure of the thermal boundary layers in a fluid with a strongly temperature-dependent viscosity we utilize an approximate method developed by fluid with a strongly temperature-dependent viscosity we utilize an approximate method developed by Howard (1966). If the upper and lower mantle have the same viscosity law, we find that stratified convection requires a lower mantle viscosity which is several orders of magnitude lower than the upper mantle viscosity. This is not consistent with studies of postglacial rebound. It is possible to obtain a viscosity law for the lower mantle that gives a viscosity nearly equal to that of the upper mantle and reasonable temperatures. However, the required law is not consistent with the currently available experimental data on lower mantle materials. Therefore we conclude that thermal arguments favor whole mantle convection.