This paper addresses the microstructural optimization of an infinite, transversely isotropic layer which is free of tractions and subjected to a prescribed thermal gradient. The layer's microstructure is characterized as a bi-phase composite in the form of a continuous matrix perfectly bonded to embedded spheroidal reinforcements. The microstructural characterization of the FGM is taken to be the volume fraction, aspect ratio and orientation distribution function of the second phase. The composite layer is made functionally gradient by taking the aforementioned parameters to vary through the thickness of the layer. The effective properties of the bi-phase composite are obtained by appropriate homogenization theories. The microstructural parameters are determined such that an objective function, defined in terms of strain energy and curvature, is minimized. Specific results are presented for an aluminum (Al) layer reinforced with silicon carbide (SiC). Comparisons are made to conventional coating technology.