Evidence for a weak San Andreas Fault includes (1) borehole heat flow measurements that show no evidence for a frictionally generated heat flow anomaly and (2) the inferred orientation of σ1 nearly perpendicular to the fault trace. Interpretations of the stress orientation data remain controversial, at least in close proximity to the fault, leading some researchers to hypothesize that the San Andreas Fault is, in fact, strong and that its thermal signature may be removed or redistributed by topographically driven groundwater flow in areas of rugged topography, such as typify the San Andreas Fault system. To evaluate this scenario, we use a steady state, two-dimensional model of coupled heat and fluid flow within cross sections oriented perpendicular to the fault and to the primary regional topography. Our results show that existing heat flow data near Parkfield, California, do not readily discriminate between the expected thermal signature of a strong fault and that of a weak fault. In contrast, for a wide range of groundwater flow scenarios in the Mojave Desert, models that include frictional heat generation along a strong fault are inconsistent with existing heat flow data, suggesting that the San Andreas Fault at this location is indeed weak. In both areas, comparison of modeling results and heat flow data suggest that advective redistribution of heat is minimal. The robust results for the Mojave region demonstrate that topographically driven groundwater flow, at least in two dimensions, is inadequate to obscure the frictionally generated heat flow anomaly from a strong fault. However, our results do not preclude the possibility of transient advective heat transport associated with earthquakes.