In this paper, we extend a recent asymptotic axisymmetric model for isothermal gas–solid flow in a countercurrent moving-bed reactor to a non-isothermal model for the heat transfer in an ironmaking blast furnace. The appended heat transfer model accounts for conduction, convection, thermal non-equilibrium between the gas and solid phases and the dominant endothermic chemical reaction in the bulk of the furnace, the Boudouard reaction. Asymptotic analysis is used to determine the leading-order heat balances and to interpret numerically obtained solutions for the phase temperatures. Although the model is considerably simpler than the many numerical models that already exist for blast-furnace operation, its future extension would form the basis of a computationally efficient approach for modelling the transient state of a blast furnace.