Abstract: A method and apparatus provides conditioning of an air stream by cooling in a regenerative heat exchanger having two groups of channels separated from one another by walls through which heat exchange occurs. The air stream to be conditioned flows through one group of channels while an auxiliary air stream flows through a second group of channels the walls of which comprise wettable material maintained wet by means of water which is caused to evaporate by the auxiliary air stream to result in cooling. The wettable material provides a substantially stationary liquid layer maintained in the channels of auxiliary air flow so that evaporation takes place directly from the walls separating the two groups of channels to obtain high heat exchange efficiency.