A mathematical model is developed for the fault zone controlled charging of a geothermal reservoir. The model is used to describe a reservoir of finite vertical extent with an impermeable upper boundary. A quasi-analytic theory is developed for high Rayleigh number convection of liquid in a rigid porous medium. In this approximation, liquid rises up the fault and spreads into the near regions of the reservoir isothermally. The cooling effect of the surface on the fault flow is confined to a thin layer near the surface. This layer grows with distance from the fault. In the far field of the aquifer the full depth of the reservoir is cooled by the surface. A study is made of the effect of various parameters such as mass flow rate, Rayleigh number, and fault width on the pressures, velocities, temperatures, and their gradients at different locations in the fault and in the aquifer. This analysis can be applied to geothermal systems where the thickness of the impermeable reservoir cap is quite small compared to the reservoir depth.