One of the promising directions for improving the environmental, technical, and economic efficiency of coal-fired thermal power plants is the use of the multicomponent fuels based on coal and combustible liquids. Such fuels, as a rule, are called coal-water slurries containing petrochemicals (CWSPs). The typical wastes of coal enrichment, low-grade coals, oil production, and oil refining wastes as well as used flammable liquids, for example oils, can be included in the fuel composition. To date, mathematical models have not been developed for predicting the effective conditions for the ignition of promising CWSPs at minimum ambient temperatures and with short ignition delay times. This problem was solved in the present work. On the basis of the experimental results, three modes of physical and chemical transformations were established when heating single particles of the composite fuel. The first one is the intensive thermal decomposition of the coal component after evaporation of the liquid components of the fuel. Then goes the gasification of coal under the boiling conditions of the liquid components followed by the heterogeneous combustion of the solid residue. The third mode is the ignition of the gas mixture in the vicinity of the fuel particle and initiation of heterogeneous combustion of the solid residue. The temperature ranges of the environment were determined under which the detected modes of the physical and chemical transformations occur. The obtained experimental data became the basis for the development of a predictive mathematical model of the transformations that occur when heating a composite fuel with different characteristics of the components. It takes into account the interrelated physical and chemical processes: inert heating, evaporation, thermal decomposition, and exothermic reaction. The developed mathematical model and the results of the theoretical studies make it possible to establish the influence of the characteristics of the fuel components and the conditions of its heating on the three identified modes of physical and chemical transformations.