The possible role of solid-state convective cooling is important in understanding planetary thermal evolution. A stable compositional stratification in planetary mantles, which can arise from partial melting due to adiabatic decompression or from early magmatic differentiation, may suppress or delay convective instability, restrict the depth scale of convective motions, and reduce the convective heat flux out of the mantle. Two-dimensional numerical experiments on convection in a stably stratified viscous fluid with a strongly temperature-dependent viscosity cooled from above are carried out to understand how convecting, well-mixed layers form and thicken in time because of cooling at the planetary surface. Simple scaling laws and parameterizations are developed that allow the results of our numerical experiments to be extrapolated to viscosity variations as large as would be expected for thermally activated creep in planetary mantles. Strongly temperature-dependent viscosity reduces the available thermal buoyancy in the cold top boundary layer and therefore increases the impact of compositional stratification. Scaling laws for the mixed layer thickening rate indicate that thickening occurs mainly by buoyant, rather than viscous, entrainment of the underlying still stratified fluid. Compositional stratification may be important in the thermal evolution of the oceanic upper mantle, formation of cratonic continental lithosphere, and in planetary evolution, more generally. In several geologically realistic settings, a restricted depth of stratification or mantle viscosities on the order of 1018 Pa s or less are required for convective instability.