The present paper discusses an analytical method for an inverse problem of three-dimensional transient thermoelasticity in a transversely-isotropic solid. The inverse thermoelastic problem consists of the determination of the condition of heating when the conditions of displacements and stresses are given at some points of the solid considered. Applying the Laplace and Fourier transforms as well as the new potential function method, the temperature, displacements, and stresses are represented by the potential functions alone, and they are determined from the prescribed conditions. The heating condition is obtained from the boundary condition for the temperature field. As a practical example of an inverse problem, the heating temperature of a transversely-isotropic infinite circular cylinder is determined in the case where the radial displacement is given at an arbitrary cylindrical section and the radial and shear stresses are free on the lateral surface of the cylinder. Numerical calculations are carried out to illustrate the heating temperature of the cylinder as well as the temperature and stresses on the lateral surface of the cylinder.

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