A method and an arrangement for air-conditioning a cold aisle which is partially bounded by heat-generating devices and is arranged in a hot room, the hot room being separated from a second room by a boundary wall, and a region of the boundary wall is formed by a heat exchanger, such that air that is conveyed through the heat exchanger by the fan is supplied to the cold aisle. An opening with a fan is provided in the boundary wall. The cold aisle is connected to the boundary wall so that the opening is surrounded by the cold aisle.