The paper presents the formulation and analysis of composite plates serving as STATs, i.e., spatially tailored advanced thermal structures where the distribution of the constituent phases varies throughout the surface as well as through the thickness. This is an extension of the well-known concept of functionally graded materials (FGM) and structures with the constituent phases varying only in the latter direction. As a result of two- or three-dimensional grading it is possible to optimize the response and properties of the structure providing multitask and multi-scale optimization. The response of plates with two- or three-dimensional grading to an arbitrary thermal loading is elucidated, including the conditions that result in thermal bending versus thermal instability.