A heat exchanger for exchanging heat between a liquid-containing medium and a gas comprises a medium inlet and a medium outlet and a flat heat exchanger mat, wherein the mat comprises a number of parallel, equidistant capillaries of heat-conducting material and wires of heat-conducting material which are attached in heat-conducting contact to the capillaries, extend in transverse direction relative thereto and have a mutual distance in the order of magnitude of the diameter of the wires, wherein gas can flow along the wires for heat exchange between this gas and the medium flowing through the capillaries, and wherein the gas flows along the mat and at least a substantial part of the gas is prevented from flowing through the mat, and the gas flows in longitudinal direction of the wires.