ESDU 89026 treats the transient situation of the variation of the temperature distribution in a thick plate insulated on one side when the aerodynamic heating temperature on the other side suffers a step change from an initial constant temperature condition. Curves are given that allow the temperatures at both the heated and the insulated surfaces to be obtained at any time, and also to obtain an approximate value for the temperature at any point through the thickness of the plate from a knowledge of those surface values. A fully worked example illustrates the use of the method.