<p>Two approaches have been developed to study the thermally stressed state of functionally graded layered shallow shells in the presence of an internal heat source. The bounding surfaces of the shell layers have zero torsional curvature, and the variability of the principal curvatures is neglected. The structure is very flat, i.e., the coefficients of the first quadratic form are taken to be equal to one. It is assumed that the radii of curvature significantly exceed the thickness of the structure, and its outer surfaces have the same curvature. The imposed constraints allowed us to reduce the curvilinear orthogonal coordinate system to a planar one. In the first approach, using Reissner’s variational principle, a system of differential equations of equilibrium is formulated. For the special case of a hinged support under conditions where the thermal load is distributed from an internal energy source according to a trigonometric law, this system reduces to a system of ordinary inhomogeneous differential equations regarding the distribution of the unknown functions over the thickness of the shallow shells. The solution is obtained analytically without introducing an approximation of the unknown functions with respect to the structure’s thickness. The second approach is based on a polynomial approximation of the unknown functions with respect to the structure’s thickness. Such an approximation accounts for shear and compression by introducing corresponding unknown functions. A distinctive feature of the approach is also the definition of the displacement functions at the outer surfaces of the structure’s layers. This makes it possible, if necessary, to divide the layers into sublayers with corresponding refinement of the calculation results. The convergence of the results obtained using the two proposed approaches confirms their validity.</p>