A simple modeling of the heat transfer through insulating bilayers of cryogenic reservoir subjected to surrounding environment or aerothermal flux is presented. The model permits to determine the instantaneous evolution of maximum fuel temperatures and the boil-off rate as well as the possible insulation ablation. To get a realistic estimation of the maximum fuel temperature and boil-off loss, the good knowledge of the internal convection coefficient, taking into account the possible fuel ebullition, is indispensable. The aerothermal flux provokes the insulation degradation and its ablation. Because of the ablation, the reservoir becomes less and less thermally protected, which may cause an important fuel boil-off. Compared to classical insulations with uniform density, those with spatially graded densities appear as potential insulations permitting to meet both light-weight and low boil-off requirements. (C) 2011 Elsevier Ltd. All rights reserved.