We apply mathematical modelling to study heat transfer processes during fire refining of blister copper in a ladle-furnace unit. A ladle-furnace unit was designed to test the refining technology using bottom blowing in a bubble mode by gaseous reducing agents (hydrocarbons) and an oxidiser. Mathematical modelling allows the properties of a real process to be described based on mathematical formalisation of physical laws and regularities. It was proposed to use gaseous reducing agents, rather than expensive residual fuel, as a liquid-reducing agent. The use of gaseous reducing agents in the bottom blowing mode produces higher technical and economic indicators of the process. In addition, some technological operations were transferred directly to the ladle, thereby eliminating the need for re-melting and heating of refined copper. One of the identified problems was the need to maintain the predetermined thermal regime, which provides the very possibility of both performing refining operations and introducing a gaseous reagent (determining the hydro-gas-dynamic parameters) into the melt during bottom blowing. An original method for considering the thermal effects of chemical reactions in mathematical models was presented using an example of exothermic reactions during oxidative refining. The use of two different methods of analysis allowed a comprehensive assessment of the influence of the main exothermic reactions on the thermal regime of the refining process. The presented mathematical models can be used for determining the specific effect of various technological parameters (composition and fuel consumption, temperature and degree of blast enrichment, lining design, etc.) on the dynamics of changes in the temperature field of the melt and the technical and economic parameters of melting as a whole.