The thermoelastic stress analysis for linear thermoelastic bodies is developed as a mathematical support to the infra-red radiometric method applied to structures under cyclic loading conditions. The author considers the relation between the temperature variation and the stress variation and takes into account the dependence of the Poisson and Young moduli of elasticity on the temperature. This relation presents coefficients which are not only the thermoelastic constant, as in the classical Kelvin formula, but depend on the average stress and on the modulus of elasticity. This result corresponds to experimental results.