In this paper, based on the identification of the law binding the decomposition of composite materials and nonlinear filtration law pyrolysis gases in the porous residue, the mathematical model and numerical method for solving the problems of the thermal state of composite materials in high-temperature conditions substantially non-stationary loading. The resulting expansion of the law allowed the binders in the problems of the thermal state of composite materials are not considered chemical kinetics in the binder decomposition. Found the law of a non-linear filtering it possible to determine the lower limit of the braking pressure pyrolysis gases, from which you must take into account the non-linear filtering. The numerical results confirm the proposed approach to the modeling of the thermal state of composite materials.