Thermal response of flat plates immersed in a fluid with oscillating temperature is of current interest in the nuclear industry. A dimensionless solution characterizing the internal temperature response shape of the plate in terms of a single dimensionless parameter has been obtained. The solution is plotted in terms of dimensionless parameters. The maximum value of surface-to-average temperature difference in the plate and the elastic stress occurring during the sinusoidal temperature cycle can be determined using this solution without plotting and averaging temperature distributions for several different times during the cycle.