In the paper, we propose an approach to solving an inverse problem of identifying material characteristics of a functionally graded thermo-piezoelectric body. The operator reciprocity equations of the first kind are obtained in order to solve the problem formulated on the basis of the iterative process. As an example, the inverse problem of thermo-electroelasticity for a pyroelectric rod is investigated. We have carried out the computational experiments on restoration of the rod characteristics with various laws of inhomogeneity including those modeling layered and functionally graded coatings. (C) 2018 Elsevier Ltd. All rights reserved.