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Herein, the effect of material inhomogeneity on the temperature and stress distributions in functionally graded solids is analyzed. Assuming the inaccessibility of the inner surface of a multilayer functionally graded hollow sphere for the direct monitoring of the temperature in real time, the problem on identifying the temperature on this surface is formulated by implementing the temperature and circumferential strain given on the outer surface. The material properties within each sphere layer are assumed to be arbitrary functions of the radial coordinate. By representing the material properties of the sphere in the form of stepwise‐variable functions and implementing the generalized derivative technique, a method for the reduction of the formulated problem to an inverse thermoelasticity problem is developed. Using the finite difference method, a numerical algorithm for solving the inverse problem is suggested. The stability of the proposed numerical algorithm concerning the input perturbation is verified.