A system for cooling a space in a vehicle comprises a sorption wheel (4), at least one heat exchanger (8), at least a first humidifier unit (10) and at least one fuel cell (6), wherein the sorption wheel (4) is adapted for drying ambient air (16) and for conveying dried process air (18) to the downstream heat exchanger (8) and the heat exchanger (8) is adapted for cooling process air (18), with the heat exchanger (8) being connected to the first humidifier unit (10) for humidifying cooled process air (20), and wherein the fuel cell (6) is connected to the sorption wheel (4) and adapted for making available fuel cell exhaust air (32) for regenerating the sorption wheel (4) and water (22) to be introduced into the first humidifier unit (10). Since the utilization of fuel cells is increasingly considered in modern vehicles and, in particular, commercial aircraft, the system according to the invention makes it possible to realize a symbiotic relationship between already installed fuel cells and cooling systems in vehicles, in which the further use of the waste products heat and humidity leads to fuel savings. In addition, an evaporative cooling method is presented, in which a fuel cell serves for supplying heat and water.