Mathematical steps leading to computation of the temperature field in multi-dimensional, multi-layer bodies are described and numerical results for two-layer bodies are presented. The presentations include boundary conditions of the first, second, and third kind. Included in this paper is a table to assist in computing eigenvalues. Also, modifications are made to account for the contribution of contact resistance. An efficient computational scheme for calculating the eigenvalues is discussed and numerical results are presented. For multi-dimensional, multi-layer bodies, the eigen-functions may have real or imaginary eigenvalues. The complete solution must include the contribution of imaginary eigenvalues; otherwise, the information will be erroneous. A procedure is introduced that places a bound on the location of each eigenvalue.