The flow of the ground water is responsible for both thermal and self-potential anomalies. Temperature is usually recorded in boreholes while self-potential is usually recorded at the ground surface of the Earth. This makes the joint inversion of temperature and self-potential data together an attractive approach to invert permeability. We use an Adaptive Metropolis Algorithm to determine the posterior probability densities of the material properties of different geological formations and faults by inverting jointly self-potential and temperature data. The algorithm is tested using a synthetic case corresponding to a series of sedimentary layers overlying a low-permeability granitic substratum. The flow of the ground water (computed in steady-state condition) is mainly localized in two faults acting as preferential fluid flow pathways. The first fault is discharging warmed ground water near the ground surface while the second fault acts as a recharge zone of cold water (a classical scenario in geothermal systems). The joint inversion algorithm yield accurate estimate of the permeability of the different units only if both temperature and self-potential data are jointly inverted. An application using real data is also performed. It concerns the upwelling of a hydrothermal plume through a set of faults and permeable formations at the Cerro Prieto geothermal field in Baja California. The optimized permeabilities are in close agreement with independent hydrogeological estimates.