Climate projections under the high-emission representative concentration pathway “RCP-8.5” scenario are used to show the effects of global warming on the energy production of two similar concentrated solar tower power plants in Spain and Chile from 2025 to 2060. Results show a reduction of the annual energy production of almost 1.8% for Chile and an increase of almost 6% in the Spanish plant, but an increase of 10% water consumption due to both the increase in dry- and wet-bulb temperatures and changes in the direct normal irradiation caused by climate change. When the effect of water restrictions is included in the model caused by the foreseen reduction in water availability in Spain, the increase of the annual energy production is only 2%. Finally, the levelized cost of energy (LCOE) calculated during the whole power plant lifetime (35 years) with respect to the LCOE obtained at the beginning of the project is increased by 1.1% in the Chilean plant, whereas in the Spanish plant, it can be reduced more than 2.5% if there are no water restrictions, while a reduction of 0.4% is expected in a scenario with water restrictions. Results show that careful consideration of climate projections should be considered to properly estimate the economic viability of solar tower plants.