A two-dimensional conceptual model of the East Mesa Geothermal system is developed on the basis of existing geological, geophysical, geochemical, heat flux, and borehole logging data. Hot water rising in a set of faults is assumed to charge the reservoir, which is overlaid by a clay-rich cap. The temperature-depth distribution observed at the site implies that the liquid is convecting at a high Rayleigh number. In this approximation, liquid rises up the fault and spreads isothermally into the nearby sections of the reservoir. The cooling effect of the surface on the flow in the reservoir is confined to a thin layer adjacent to the cap-reservoir interface near the fault. This layer grows with the distance from the fault. Eventually, the entire depth of the reservoir is cooled by the surface. The mathematical model is based on the flow of liquid water in a saturated porous medium. Results are obtained for the velocities, pressures, and temperatures in the entire system consisting of fault zone, aquifer, and clay cap. Finally we compare the predicted surface heat flux to that measured at the site in shallow wells. It is concluded that the model represents a plausible description of fault zone controlled systems like that at East Mesa.