Axisymmetrical thermoelastic singular stress problems for a nonhomogeneous infinite body and thick plate are considered, theoretically. It is assumed that the nonhomoge neous material properties of shear modulus of elasticity G, the coefficient of linear thermal expansion alpha, and the thermal conductivity lambda vary with the axial coordinate z according to the power product form. As an analytical model, a nonhomogeneous infinite body and thick plate with a penny-shaped crack subject to an arbitrarily distributed axisymmetrical heat supply on its crack surface are considered. The distributions of the displacement component and the stress component are analyzed using the fundamental equation system proposed in our previous paper, and the thermal stress intensity factor at a crack tip is evaluated theoretically. Numerical calculations are carried out for several cases taking into account the variety of nonhomogeneity of G, alpha, and lambda. Thereafter, the distributions of the displacements, stresses, and thermal stress intensity factor at the crack tip are shown graphically, and the influence of these nonhomogeneous material properties on the thermoelastic field and the thermal stress intensity factor is discussed.