The article presents the results of theoretical and experimental studies of the ignition process of coal fuel particles in a pelletized state during high-temperature radiation-convective heating in an oxidizing environment. A new, different from the known, “two-temperature” mathematical model of the ignition process of a cylindrical coal pellet under intense heating conditions is presented. During the modeling, a detailed kinetic scheme of the reaction of gaseous products of thermal decomposition of coal with atmospheric oxygen was considered. The mathematical model was tested through a comparative analysis of the theoretical and experimental values of the ignition delay times of coal pellet fuel with experimental data. A wide range of heating conditions that could potentially lead to solid-phase ignition were analyzed. The research results showed that even under conditions of high oxygen content in the original coal, solid-phase ignition of coal pellets does not occur during intense heating. Based on the results of numerical modeling, it was established that the ignition process occurs in the gas phase. The oxygen released during the thermal decomposition of coal is not enough for stable gas-phase or heterogeneous ignition of pyrolysis products in the intrapore space of the fuel pellet. Based on the results of the numerical modeling, it was established that the oxygen released during the thermal decomposition of coal is significantly deficient in the intrapore space. The O2 concentration is not enough for a significant (in terms of heat flow) thermochemical intrapore reaction with gaseous and solid products of thermal decomposition.