We study the thermal stability of layered orthotropic shell, reinforced by an elastic hollow cylinder and poliregulyarnoy system of longitudinal ribs. Functions movements hinged shell and cylinder are presented in the form of trigonometric series in the circumferential coordinate. To obtain the characteristic equation using the method of successive elimination of entire groups of unknowns, corresponding to the same edges of the overall system of the original equations. As a result, the problem reduces to a system of three algebraic equations for the two displacement components and functions of the base shear edges of the system. The vanishing of the determinant of the system gives the critical temperature. In the numerical example shows the effect of heating of individual groups of ribs on the critical temperature.