A mathematical model was developed to predict heat transfer from the freeboard gas to the bed of a rotary kiln. The thermal model incorporates a two-dimensional representation of the bed’s transverse plane into a conventional one-dimensional, plug flow model for rotary kilns. The result, a quasi-three-dimensional rotary kiln model, significantly improves the ability to simulate conditions within the bed without the necessity of rigorously accounting for the complex flow and combustion phenomena of the freeboard. The combined model is capable of predicting the temperature distribution within the bed and the refractory wall at any axial position of the kiln.