The thermal resistances of the slag films and the air gap between the slab and the mold are important factors in heat transfer and lubrication control inside a continuous casting mold. The formation, evolution, composition and distribution of the slag film and air gap have significant influences on the initial solidification of the strand shell and slab quality. In this paper, based on experimentally measured thermocouple data and casting conditions, an inverse problem model of mold heat transfer is developed, with the purpose of accurately predicting the mold heat transfer states and slab solidification processes of actual casting conditions. Furthermore, a numerical model of the heat transfer between the air gap and the liquid/solid slag films is developed, based on analysis of the formation mechanism, distribution and heat transfer characteristics of the air gap and slag films. The non-uniform distribution of the thermal resistance of the air gap and the liquid/solid slag films, and the heat conduction and heat radiation inside them are simulated, which provide a theoretical foundation for exploring the complicated heat transfer behavior and surface crack prediction during the continuous casting process.