A transient plane-stress thermoelastic problem in a nonhomogeneous hollow circular plate of variable thickness is formulated in terms of a stress function by deriving new Michell integral conditions necessary for the assurance of single-valuedness of rotation and displacement. An analytical solution is presented for thermal stresses in a nonhomogeneous hollow circular plate subjected to unaxisymmetic heating on the boundary surfaces, which has the plate thickness, Young's modulus and thermal conductivity in forms of different power laws of the radial coordinate; the coefficient of linear thermal expansion is given as an arbitrary function of the radial coordinate. Numerical calculations are carried out over a wide range of the nonhomogeneous thermal conductivity, Young's modulus, coefficient of linear thermal expansion and plate thickness. The effects of nonhomogeneous thermal and mechanical properties on the relaxation of thermal stress and its application to the design of functionally gradient materials (FGM) are discussed.