A mathematical framework is developed for studying the heat transfer through the metallic wall of an internally heated rotating drum of a drum dryer. Contrary to the few earlier analyses that solved numerically the transient two-dimensional partial differential equation of heat conduction until a cyclic steady state is reached, the present analysis transforms it to a one-dimensional integral equation that can be solved directly for the cyclic steady state. In this new formulation the thermal inertia of the wall is directly assigned to specific terms of the kernel of the integral equation which makes the assessment of its contribution very easy. A numerical method for the solution of the integral equation is developed. An approximate solution method based on polynomial expansion is developed, too. Results from the different solution approaches of the effect of thermal inertia on the response of the dryer are discussed for both simplified and realistic cases. (C) 2003 Elsevier Ltd. All rights reserved.