In determining temperature stresses in anisotropic viscoelastic and thermologically simple bodies the assumption of uniformity of a nonstationary temperature field T(r, t)=T(t) has allowed to use the Laplace transform in reduced time ξ scale. To obtain accurate data, the cooling process should be divided into a number of successive intervals in each of which its time scale has been specified with an appropriate recalculation of the viscoelastic functions. Kinetics of the temperature stresses in a thick-walled orthotropic ring of fibreglass plastics has been calculated. The numerical data obtained with the Laplace transform and the finite difference methods have proved to agree well. A similar estimation of residual stresses can be obtained by an instantaneous glass-transition model.