ESDU 89025 treats the transient condition of the variation of the surface stresses in 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 stresses to be obtained at both the heated and insulated surfaces at any time for a plate with completely free edges. The curves can be applied when there is a thin insulating layer at the heated surface. A fully worked example illustrates the use of the method.