A wet-surface heat-exchanger, where the effluent air is moistened, is analysed according to a thermodynamic theory and data of experimental tests. An entropy generation function, which takes into account the changes of temperature and humidity of air, is derived. The analyses show that it is thermodynamically possible, without any cooling machine, to achieve extremely large temperature drops. With certain parameters the system results in a maximum rate of entropy generation which is used to analyse differences between two different methods of spraying the moistening water. Approximal limits for the efficient working fluid mass flow value are also given.