Rotary kilns are employed by industrial site to carry out a wide variety of material processings; calcining limestone, reduction of oxide ore,etc. In this study a mathematical model was developed to predict heat transfer from the freeboard gas to the bed of a rotary kiln. This presents a three-dimensional mathematical model to describe and simulate the calcination of solid bed in a rotary kiln. The model comprises conventional differential equations derived from the principles of conservation of mass and energy and this can be used to predict the temperature profiles of the solid bed, the gas phase and inner wall of the kiln along the length of the kiln axis and in radial direction. The major parameters considered here are kiln rotation rate(rpm), filling ratio of the solid bed, burner injection-temperature. The results from the simulation showed reasonable agreement with experimental results available in the literature.