Abstract: In order to obtain a fine-lamellar perlite structure in the edge region of the heads of rails (1), especially hot-rolled rails for carriageways or railways, by specific thermal treatment during cooling from the rolling heat without the formation of bainite, precooling (12) occurs in order to achieve a core temperature of approximately 750 - 850° C., and the temperature of the more intensively cooled edge region is raised by intermediate heating (13) to at least said core temperature and finally cooled (14).