A method for determining time-optimum medium temperature changes is presented. The heating and cooling of the pressure elements will be conducted in such a way that the circumferential stresses caused by pressure and fluid temperature variations at the edge of the opening and point of stress concentration do not exceed the allowable values. However, the calculated optimum temperature changes are difficult to follow in practice during the initial stage of heating. Nevertheless, it is possible to increase the fluid temperature stepwise to the minimum value and then heat the pressure component according to the determined optimum temperature changes. Allowing stepwise fluid temperature increase at the beginning of heating ensures that the heating time of a thick-walled component is shorter than the heating time resulting from the calculations according to EN 12952-3 European Standard or TRD 301 (Technische Regeln fur Dampfkessel) regulations. Copyright (C) 2010 John Wiley & Sons, Ltd.