ESDU 89023 treats the transient situation of the variation of the temperature distribution through a thick plate insulated on one side when the aerodynamic heating temperature on the other side is changing@ from an initially constant temperature condition@ linearly with time. Curves are given that allow the temperature change from the initial constant temperature condition to be obtained at both surfaces and at three surfaces at equal +intervals through the plate. The method can be applied also when there is a thin insulating layer at the heated face. A fully worked example illustrates the use of the method.