Pattern distortion caused by resist heating can be a significant contributor to errors in feature size and pattern placement. The Green's function method is suitable for determining the temperature evolution during resist exposure, but the previous published solutions are based on different simplifications and lead to different results. In this paper we present a solution of the multi-layer Green's function with clearer physical meaning. This model takes into account the thermal diffusion in all layers of resist chromium and substrate and can be used to calculate the four-dimensional temperature profiles that exist during and after electron beam exposure. Different writing strategies can cause differing degrees of edge displacement and this can lead to errors in feature size and feature position and to edge roughness.