This study carries out the thermal residual stress analyses of functionally graded clamped hollow circular plates for in-plane constant inner and outer edge heat fluxes. The material properties of the functionally graded plates were assumed to vary with a power law along an in-plane direction not through the plate thickness direction. The transient heat conduction and Navier equations describing the two-dimensional thermoelastic problem were discretized using finite difference method, and the set of linear equations were solved using the pseudo singular value method. In order to determine the effect of the plate material properties on the thermal deformation and stress states the circular plates were designed in the way that their material compositions can vary from a pure ceramic (C) outer edge to a pure metal (M) inner edge and vice versa, such as ceramic-to-metal or metal-to-ceramic circular plates. The compositional gradient and direction affected considerably both in-plane temperature levels and heat transfer period whereas similar temperature distributions existed. The displacement components exhibited similar symmetrical distributions and were at lower levels in the metal-rich compositions. The normal strain components had similar distributions to those of the displacement components and were critical around both the inner and outer edges. A metal-rich composition resulted in lower normal strain levels. The equivalent strain distributions were always critical around the heat flux edge and became highest for a ceramic-rich composition. The normal stress components and equivalent stresses were critical in the ceramic-rich regions and the equivalent stress exhibited a sudden increase near the pure ceramic-edge subjected to the heat flux. The lower stress levels were also observed for a metal-rich composition variation. The ceramic material, a good thermal insulator, makes a metal-to-ceramic and a ceramic-to-metal material system suitable for outer and inner edge heat fluxes, respectively in practice. The metal-rich material compositions (with n = 0.1 and 10.0) can prevent the local cracks in the ceramic-rich regions induced by high heat gradients.