Analysis of Martian gravity and topography implies that crustal thickness variations created in the earliest evolution of planet have persisted to the present day. Relaxation of crustal thickness variations due to lower crustal flow by thermally activated creep is strongly temperature-dependent and so, for particular crustal rheology and thickness, provides a constraint on thermal evolution. Previous models have assumed that the heat flux from the mantle, which controls lower crustal temperatures, simply reflects radiogenic heat production. However, global thermal evolution models in which the mantle cools by solid-state thermal convection indicate that the additional contribution to near-surface heat flux due to secular cooling significant increases lower crustal temperatures. With, a 50-km-thick crust, and a wet diabase rheology, these higher temperatures allow crustal rock to flow fast enough to relax crustal thickness variations during the first ~750 Myr of evolution. Previous studies have not considered the presence of an impact-brecciated crustal layer that would almost certainly be present on early Mars and could have a significant influence on crustal temperatures. The presence of a dry brecciated crustal layer several kilometers thick would significantly increase the temperature of the lower crust resulting in more rapid relaxation of crustal thickness variations. If the porosity of a brecciated crust is water saturated, then the effect of such a layer is greatly reduced. However, if water is present, cooling of the upper crust by groundwater convection in a deeper impact-fractured crustal layer with modest permeabilities could reduce lower crustal temperatures enough to explain the preservation of ancient crustal thickness variations. A cooler lower crust is also possible if solid-state thermal convection in the mantle is inhibited by a stable compositional stratification resulting from the fractional solidification of an early magma ocean.