Abstract: In a method of cooling a hot surface, a liquid cooling medium is atomized by a plurality of nozzles in a hollow space surrounding the surface and open towards the atmosphere. In order to ensure uniform continuous, yet just sufficient, cooling of the hot surface, with the cooling effecting with a constant temperature as possible over an extended period of time while avoiding changing thermal expansions of the hot surface, the liquid cooling medium is continuously atomized by means of unary nozzles to a fine mist having a droplet size ranging between 4 and 60 .mu.m. The mist leaves the unary nozzles at a low speed and is moved along the hot surface within the hollow space surrounding the hot surface under utilization of the natural thermal current in the hollow space.