On stagnant-lid planets, the crust is not recycled by subduction and can grow thick enough to significantly impact mantle convection. We perform numerical models of stagnant-lid convection to determine new scaling laws for convective heat flux that specifically account for the presence of a thick buoyant crustal layer, or the ``thick crust limit," where the crustal thickness determines mantle properties. We find that smaller planets are more likely to enter the thick crust limit.