Approximate closed-form solutions are obtained for the thermal stress and deformation of an orthotropic layered shell of revolution with properties that vary along the meridian and through the wall thickness. The shell is subjected to axisymmetrical temperature as well as surface load distributions. Particular solutions of the governing differential equations give significant bending stresses that can occur far from the supporting edge of the shell, due to the nonhomogeneity of the shell wall. The asymptotic results presented in this paper for the orthotropic shell of general meridian reduce exactly to the classical thermal solutions obtained by Timoshenko for the isotropic cylindrical shell.