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.