The mathematical formulation of the steady-state temperature field in multi-dimensional and multi-layer bodies is presented. The numerical examples are for two-layer bodies and they include boundary conditions of the first, second, and third kind. This study includes tables to assist the selection of eigenfunctions and computation of the eigenvalues. The computations include the contribution of contact resistance to the temperature solution. An efficient computational scheme for calculating the eigenvalues is used. For multi-dimensional, multi-layer bodies, the eigenfunctions are real if each layer is homogeneous; they may become imaginary if layers are orthotropic. (C) 2003 Elsevier Science Ltd. All rights reserved.