The objective of this presentation is the development of a generalized steady-state Green's function solution to study the temperature field in moving bodies. This type of solution permits the inclusion of different non-homogeneous boundary conditions, volumetric heat sources, and possible position-dependent thermophysical properties. Although the mathematical formulation is for moving solids, it can be used to study the heat transfer in a moving fluid with a non-uniform velocity distribution passing through a micro-channel or fluid-saturated porous ducts. Additionally, this presentation includes the application of this Green's function solution to acquire numerical information for selected examples to further illustrate the numerical details. (C) 2010 Published by Elsevier Ltd.