Based on the Donnell theory of shells combined with the von-Karman type of geometrical nonlinearity, three coupled equilibrium equations for a through-the-thickness functionally graded cylindrical shell embedded in a two parameter Pasternak elastic foundation are obtained. Equivalent properties of the shell are obtained based on the Voigt rule of mixture in terms of a power law volume fraction for the constituents. Properties of the constituents are considered to be temperature dependent. The temperature profile through the shell thickness is obtained by means of the central finite difference method. Linear prebuckling analysis is performed to obtain the prebuckling forces of the cylindrical shell. Stability equations are derived based on the well-known adjacent equilibrium criterion. Three coupled partial differential stability equations are solved with the aid of a hybrid Fourier-GDQ method. After validating the numerical results, some parametric studies are conducted to investigate the influence of various parameters, especially foundation interaction. It is shown that elastic foundation enhances the critical buckling temperature difference of the shell and violates the buckled pattern.