A 2D transient mathematical model is proposed to analyse a gas rotary furnace intended for melting a CaO-SiO2 slag, a crucial component to be used in the aluminothermic reduction for silicon production. The research, conducted in the framework of the EU SisAl Pilot project, aims to assess the feasibility of the industrial process of these furnaces and to recommend potential scale-up strategies. The mathematical model addresses two distinct but related issues. First, one problem is dedicated to the evaluation of the gas combustion characteristics, including the simulation of the natural gas flame as well as the heat transfer by convection and radiation. Secondly, the temperature data computed on the inner wall of the rotary kiln is used as a boundary condition to solve the problem of melting the solid material, thus determining the required melting time. The model is validated against experimental data for the melting of iron, the material currently used in the plant.