Because of enormous applications of composite materials, functionally graded materials in industry and in various engineering designs like aerospace, submarine structures, civil engineering structures have been increasing interest to Scientists and Engineers. The advantages of composite materials over the traditional materials lie on their valuable strength, elastic and other properties. These types of materials reduce not only residual and thermal stresses but also increase the bonding strength and toughness as well. It has been proved that properly treated composite materials or functionally graded or non-homogeneous materials are the better choice for their strength and stability in respect of isotropic and homogeneous materials. Trying to highlight on the heat transfer phenomena on deformable bodies, and to address various generalization of heat conduction have been presented in this book. Various generalization of the coupled thermoelastic models have been presented subjected to different medium and vbased on geometry of the problem. Noteworthy significance of such heat conduction is addressed and its importance is also highlighted during the fabrication process of FGM.