Thermal shape relaxation of systems with self-similar surface is studied using three-dimensional Monte-Carlo simulations. In the generic example where the two main thermal diffusion mechanisms act with about the same strength, the self-affinity of the structure yields unexpectedly the two thermal processes not to act identically following the place in the structure. More precisely, evaporation-deposition events appear to govern the behavior of the active surface, while surface diffusion is the main process involved in bulk shrinkage. It results in the natural dynamic enhancement of themorphology differences between the surface and the bulk, before effective flattening of the surface may occur. (C) 2009 Elsevier B.V. All rights reserved.