The simulation of the chip heating process in the zones of gas-flame and induction heating of a continuous muffle furnace has been carried out. The mechanisms of heat transfer (conductive, convective, radiative) that have a conjugated character are considered in the approximation of interpenetrating continuums in the absence of any noticeable influence of filtration processes under conditions of a highly porous chip medium. As a result of the analysis of heat and mass transfer in the porous chip body and the working space of the furnace, a system of equations was obtained for calculating temperature and concentration fields and fields of thermal radiation intensity depending on the specified furnace productivity, natural gas consumption, and oil concentration in the coolant. The system of equations, which is a model of heat and mass transfer processes, is closed and allows us to solve the problem posed – to determine the heating temperature of the chips at the exit from the gas-flame heating zone, the composition and residual content of the liquid phase in it, and also to find the optimal height and temperature of the inductor muffle in induction heating zone, dimensions and electrical parameters of the inductor.