Geothermal exploitation systems consisting of parallel vertical hydraulic fractures might be used to flush heat from porous rock formations with permeabilities in the tens of millidarcy range. Such systems are analyzed using the conservation equations to find the temperature history of the fluid produced, the thermal power output, and the fraction of the heat recovered, in terms of the applied pressure drop, the permeability, the anisotropy of the medium, and the scale over which the permeability is effectively homogeneous. In effectively homogeneous media, a thermal front is driven outward from the injection fracture. Rock outside this boundary is hot; within it is cool; for flows with P¿clet numbers over 100 the front itself is sharp. The shape of the cooled region depends strongly upon the anisotropy of the medium. The variation of permeability is suitably scaled and related to the P¿clet number to elucidate those cases which are favorable for geothermal exploitation. For a range of reasonable parameters the power output is more than three times that obtained using boreholes not having hydrofractures to extend the collection and reinjection surfaces.