A general solution of the heat conductivity and quasi-static thermoelasticity problems for a twolayer orthotropic cylindrical shell was obtained. Expressions for the integral characteristics of the temperature for the shell, which is locally heated by a temperature field or external environment by means of convective heat transfer at the initial moment of time, were recorded. The temperature and stress and strain state of the considered shell of a finite length depending on the physical parameters that corresponded to the thermophysical and mechanical characteristics of the materials of the constituent layers of the shell were studied, as were the geometrical parameters that determined the area of the local heating and heating time.
