In this paper, the process of flowing the coolant gas through granular or porous media with heat-generating sources is considered. Such process takes place in various ruinous objects with energy release sources formed after natural or man-made disasters, e.g., in destroyed power unit of a nuclear power plant like exploded reactor No. 4 of the Chernobyl NPP. Also, this process is typical for some technologies, e.g., for innovative pebble-bed nuclear reactors. The aim of this work is, firstly, to develop a tool for numerical simulation of 3D processes in porous media with energy release sources, which will allow one to get the proper results quickly, and, secondly, to study some important features of these processes. A computational model and OpenFOAM solver have been developed in the work to simulate the fluid flow and heat transfer in granular or porous energy-releasing materials. The proposed mathematical model is based on the assumption of interacting interpenetrating continua, and the developed numerical method is based on the PIMPLE algorithm adapted for the system of governing equations. The novel OpenFOAM solver has been tested on 1D and 2D problems, which were previously solved by known algorithms based on the finite difference method. The new solver is faster by 1–3 orders of magnitude (depending on the number of cells in the mesh) and makes it possible to carry out calculations of 2D and 3D processes without parallelization within reasonable time, in contrast to the previously used numerical methods. The 3D gas flows through porous energy-releasing object have been studied, and some important features of these processes have been revealed. It has been shown that the temperature dependence of the gas dynamic viscosity leads not only to the fact that the gas tends to flow around the hot zones, but also to an additional increase in temperature in the heated area, caused by a drop of the density and velocity of the gas due to increasing the flow resistance force in this region. It has been revealed that if the total intensity of the energy release in the porous object is known a priori, but the relative location of the energy release sources is unknown, it is impossible to predict the maximum temperature of the object.