Method and device for cooling circulating air

Circulating air is cooled by heat exchange with adiabatically cooled process air. To this end, a first heat exchanging device is fed with circulating air and the process air. The heat exchanging device contains a humidifying device used to spray water into the process air. In this way, the process air is adiabatically cooled and the corresponding cooling is carried out by heat exchange with the circulating air. Before entering the first heat exchanging device and before leaving same, the process air is guided through a second heat exchanging device in which the cooled process air first extracts heat from the uncooled process air. This increases the cooling performance of the device.