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In this study, a general analysis of one dimensional steady-state thermal stresses of a functionally graded hollow spherical vessel with spherical isotropy and spherically transversely isotropy is presented with material properties of arbitrary radial non-homogeneity. The material properties may arbitrarily vary as continuous or piecewise functions. The boundary value problem associated with a thermo-elastic problem is converted to an integral equation. Radial and tangential thermal stress components distribution can be determined numerically by solving the resulting equation. The influence of the gradient variation of the material properties on the thermal stresses is investigated and the numerical results are presented graphically.