The failure of the thermal protection structure is very important to the safety of the aircraft structure. In order to accurately predict the flexural behavior of the aerogel sandwich thermal protection structure, first of all, for the sandwich structure in the form of statically indeterminate beam with variable cross-section, the beam theory considering the transverse shear deformation of the core layer was deduced. Secondly, by comparing the deflections, the forms of deflection curve and the maximum strains of the upper panel, the accuracy of the theoretical prediction was analyzed. Then, according to the requirements of heat protection and integrity of the thermal protection structure, the optimization analyses of the parameters of the core layer, such as the thickness, the density and the elastic modulus, were carried out. The results showed that the beam theory considering the transverse shear deformation of the core layer had better prediction accuracy. The maximum deflection error was the smallest, which was -17%, and the form of the deflection curve was the most reasonable. Within the range of the physical parameters of the core layer studied, the theoretical basis and guiding direction were given for the regulation of the performance of the aerogel core layer.