The use of geothermal energy is expected to grow rapidly over the next several decades at many places in the world, since geothermal resources are abundant, and because this renewable energy option is both a low-carbon and non-intermittent technology. With the integrated assessment model TIAM-ECN we quantify how large its growth could be until 2050, and analyze how this expansion could be stimulated by both climate policy and technological progress. We inspect both geothermal energy's main applications: the generation of electricity and the production of heat. For the former, we project an increase to a power production level of around 800-1300 TWh/yr in 2050, depending on assumptions regarding climate ambition and cost reductions for enhanced geothermal resource systems. For the latter, with an emphasis on residential and commercial heat use applications, we anticipate under the same assumptions a rise to about 3300-3800 TWh/yr in the same year. We estimate that by 2050 geothermal energy plants, partly in competition with renewables like solar and wind power, as well as with incumbent fossil fuel based power production, could contribute approximately 2-3% to global electricity generation. If all nations stay on track of the Paris Agreement target by not increasing the global average atmospheric temperature with more than 2 degrees C, and if the costs of geothermal energy production from deep formations reduce with the same learning rate of 13% that has been empirically observed for fracking technology applied to natural gas fields, we project a possible total geothermal energy investment market (supply plus demand side) worth about 500 billion US$/yr by mid-century.