Topographic profiles across a lobate fault scarp on Mercury have been used to constrain the depth of faulting to 30--40 km. Here we use this depth to place constraints on the crustal thickness and heat flow into the base of the crust. With no crustal heat production, the mantle heat flux on Mercury at the time of scarp formation was 30--50 mWm-2. However, higher crustal heat production rates allow significantly lower mantle heat fluxes. In all cases the mantle heat flux exceeds the likely radiogenic heat flux 4 Gyr ago; it is likely that secular cooling accounted for the remainder. Irrespective of crustal heat generation, a crustal thickness of ≤140 km is required to satisfy both the faulting observations and the requirement that the base of the crust does not melt. The effective elastic thickness of the lithosphere at the time of faulting is predicted to be 25--30 km.