A heat recovery from humid exhaust air by a simple condensation of the water vapor contained, is particularly at higher moisture contents, often economically and contributes to the rational use of energy. If the useful temperature level is higher than the water vapor dew point, the dew point has to be increased accordingly. For that purpose advantageous open absorption heat pumps can be used. However, the required additional apparatus degrade the economy and is largely caused by the absorber. Conventional absorbers work in (uncooled) counter-current regime and due to the flooding point problem, only low gas speeds can be selected. On a pilot plant has been demonstrated, that a considerable increase in gas speed when using the (cooled) co-current principle is possible, and the absorber may be carried out by significantly smaller.