When the temperature of the external surface of a wall increases, it is important to predict what the thickness of the wall will be so that the internal surface of the wall does not exceed a limit value. We will study, by an analytical method, the case in which the external surface temperature is linearly varying with time in order to determine the time for which the temperature does not exceed a predetermined limit value at a given depth from the surface. Two cases will be considered: the first one is for a wall made of a homogeneous material (e.g. concrete) and the second one is for a wall made up of concrete and phase-changing material whose melting temperature will be selected according to the desired temperature. The results obtained show that a significant delay to reach this temperature can be obtained between the two cases.