The physical and mathematical models of heat and mass transfer at the heating of a water droplet with carbonic inclusion in a high-temperature (more than 800 K) gas area in a flaming field of combustion are presented in the work. The physical and mathematical formulations of the heat and mass transfer problems under conditions of phase transformations are reduced. The methods of numerical solution of the set problem are described. The numerical investigations for the wide range of parameters of the system "heterogeneous water droplet with a solid inclusion - high-temperature gas area" were conducted. Two modes of phase transformations were indicated in the concerned system: the mode of formation of "flash" vaporization centers in a field of the contact between solid inclusion and liquid (at a temperature of gas area Tf > 1050 K and a radius of heterogeneous droplet r2 > 0.3 103 m) and the mode of liquid evaporation from the free droplet surface into the field of high-temperature gases (at Tf < 1050 K and r2 < 0.3-10-3m). The distributions of temperature corresponding to each of revealed modes of phase transformations were presented. The comparison of numerical simulation results with the results of conducted before experimental investigations of evaporation of water droplets with solid inclusions during motions in a "flame" combustion field was carried out. A good agreement with the results of numerical calculation using the developed model and the results of experimental investigations was revealed.