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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 nonhomogeneous 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.