A one dimensional mathematical model for the rotary cooler based on the energy balance equations was developed to analyze the heat transfer phenomena and to predict the effects of operating variables on the performance of rotary cooler at steady state. The input and output temperatures of gas measured at the charge and discharge ends of rotary cooler were used as boundary conditions for the differential equations. Temperature distributions of solid, gas and wall were obtained by solving two differential equations and two algebraic equations under the constraint of two point boundary conditions and operating conditions of the rotary cooler. The temperatures of outer wall calculated by the model were in good agreement with those measured at the running rotary cooler for the alumina.