An evaporative heat exchanger is provided with a working channel that has primary and secondary surfaces and a plurality of product channels. The product channels have primary and secondary surfaces. A liquid supply provides an evaporative liquid to the secondary surfaces. A product fluid may circulate through the product channels in heat exchanging contact with the primary surfaces thereof. The primary surface of the working channel is in flow communication with the secondary surfaces of both the working channel and the product channels such that a working fluid may flow first over a primary surface of the working channel and subsequently over the secondary surfaces where it absorbs liquid by evaporation.