The present invention relates to a method of cooling strip or wire products in which, subsequent to being annealed, the product (3) is cooled to a temperature of about 20-50°C beneath its oxidation temperature. The invention is characterised by winding the product (3) around a drum (1) immediately downstream of an annealing path so that the product (3) is brought to lie in mutually juxtaposed turns and thereafter to be unwound from the drum (1) after a number of turns, wherein the product is wound onto the drum (1) through a number of turns such that said product (3) will be cooled to a desired temperature, and wherein the drum (1) is given a diameter that exceeds the diameter at which the product (3) will be influenced mechanically by plastic deformation.