Equations are given for determining transient and residual thermal stresses in a heat-treated plate. The material of the plate is assumed to be elastic, perfectly plastic. The temperature is assumed uniform on any plane parallel to the faces of the plate but can vary arbitrarily in the direction normal to the face and in time. The stress distribution during the unloading period is determined exactly without the simplifying assumption of simultaneous unloading. Application is made to the determination of stresses during cooling of a uniformly heated plate. The stress-distribution sequence and residual stresses are calculated for several values of cooling rate and yield stress.