Abstract Surface heat flows are calculated from elastic lithosphere thicknesses for the heavy cratered highlands of Mars, in terms of the fraction of the surface heat flow derived from crustal heat sources. Previous heat flow estimations for Mars used linear thermal gradients, which is equivalent to ignoring the existence of heat sources within the crust. We compute surface heat flows following a methodology that relates effective thickness and curvature of an elastic plate with the strength envelope of the lithosphere, and assuming crustal heat sources homogeneously distributed in a radioactive element-rich layer 20 or 60 km thick. The obtained results show that the surface heat flow increases with the proportion of heat sources within the crust, and with the decrease of both radioactive element-rich layer thickness and surface temperature. Also, the results permit us to calculate representative temperatures for the crust base, rock strength for the upper mantle, and lower and upper limits to the crustal magnetization depth and intensity, respectively. For Terra Cimmeria, an effective elastic thickness of 12 km implies between 30% and 80% of heat sources located within the crust. In this case the uppermost mantle would be weak at the time of loading, and temperatures in the lower crust cold enough to favor unrelaxed crustal thickness variations and to permit deep Curie depths in the highlands, as suggested by the observational evidence.