Forest fires have a negative impact on the functioning of the railway. The aim of the work is a mathematical modeling of heat transfer in the structures of a passenger carriage under the influence of radiation from a forest fire front. The originality of the study is explained by modeling heat transfer in structural materials of a passenger carriage under the influence of radiation from a forest fire front. Low and high intensity surface forest fires, crown forest fires are considered. Most of the previously published works are devoted to the analysis of the causes of forest fires, including the ones near the railway. The software implementation of the mathematical model is performed in the RAD Studio software in the high-level programming language Delphi. Mathematically, heat transfer in the materials of a passenger carriage is described by nonstationary differential heat conduction equations with corresponding initial and boundary conditions. In order to solve the partial differential equations, the finite-difference method and the locally one-dimensional method are used. Difference analogs of differential equations are solved by the marching method. The main findings of the study are: 1) physical and mathematical models of heat transfer in the structures of a passenger carriage under conditions of exposure to radiation from a forest fire; 2) the obtained temperature distributions in the inhomogeneous structure of the passenger carriage wall; 3) simulation has shown that a low-intensity surface forest fire causes a relatively safe forest fire impact scenario, while a high-intensity surface forest fire impact is a potentially dangerous scenario; 4) the scenario of the impact of a crown forest fire is unambiguously dangerous at any parameters; 5) the results obtained in this paper and the expected in future investigations will create a physical basis for the development of software for fire safety systems for rolling stock on the railway. The presented results are proposed to be used for forecasting, monitoring, and assessing forest fire dangers during the operation of the rolling stock of JSC Russian Railways.