Models of hydrothermal groundwater circulation can quantify limits to the role of hydrothermal activity in Martian crustal processes. We present here the results of numerical simulations of convection in a porous medium due to the presence of a hot intruded magma chamber. The parameter space includes magma chamber depth, volume, aspect ratio, and host rock permeability and porosity. A primary goal of the models is the computation of surface discharge. Discharge increases approximately linearly with chamber volume, decreases weakly with depth (at low geothermal gradients), and is maximized for equant-shaped chambers. Discharge increases linearly with permeability until limited by the energy available from the intrusion. Changes in the average porosity are balanced by changes in flow velocity and therefore have little effect. Water/rock ratios of ~0.1, obtained by other workers from models based on the mineralogy of the Shergotty meteorite, imply minimum permeabilities of 10-16 m2 during hydrothermal alteration. If substantial vapor volumes are required for soil alteration, the permeability must exceed 10-15 m2. The principal application of our model is to test the viability of hydrothermal circulation as the primary process responsible for the broad spatial correlation of Martian valley networks with magnetic anomalies. For host rock permeabilities as low as 10-17 m2 and intrusion volumes as low as 50 km3, the total discharge due to intrusions building that part of the southern highlands crust associated with magnetic anomalies spans a comparable range as the inferred discharge from the overlying valley networks.