This paper presents a closed form solution of the biharmonic differential equation for the bending of a thin circular plate, which is kinematically supported and subjected to a generalized non-uniform thermal moment distribution. From this solution, normalized performance curves are developed for nonuniform thermal bowing and the ensuing RMS figure errors in flat circular mirrors. Several test cases of the closed form solutions were compared with independent Nastran based finite element solutions, and practically exact correlation between the two was obtained in all the cases. However, an analytical approach based on the closed form solution is significantly more efficient and cost-effective. The methodology of the closed form solution is not limited to flat circular mirrors. Some illustrative examples are included here from a similar, but somewhat more complex, closed form solution for curved circular mirrors.