Natural convection flows in open-loop thermosyphons are examined. The thermosyphons are embedded in an impermeable medium which is heated uniformly from below. The thermosyphon loops charge and discharge fluid at a horizontal boundary of the medium. The impermeable medium is of high thermal conductivity and the temperature of both the medium and the thermosyphon walls increases linearly with depth. Analytical and numerical solutions are presented for a range of thermosyphon geometries. Critical Rayleigh numbers for the onset of motion are determined. A maximum exit temperature is found for elliptical-open-loop thermosyphons. Higher exit temperatures require long residence times at depth. Results are applicable to the cooling of porous materials and to hydrothermal circulations in the oceanic and continental crusts.