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A problem of elasticity of cylindrical shell made of orthotropic different resistant material is considered in this article. The problem is uncoupled, i.e. it consists of two separate problems: of structural mechanics and of thermodynamics. The article contains research of a shell within the framework of shallow shells theory. The solution is based on the technical hypotheses of Kirchhoff-Love. The relations of Treschev A.A. are used in the capacity of physical dependencies. The main relations are used in the form of the elastic solutions method of Ilushin A.A. The process of heat transfer is described by classic equation of heat conductivity. The article introduces a system of solving equations in combined form supplemented by initial conditions and boundary conditions.