In this article, the analysis and research of the free vibrations of the fiber metal laminate(FML) cylindrical shell under the influence of temperature is investigated. The influence of heat can cause significant changes in the vibration behavior and dynamic response of the structure. The purpose of this research is to investigate the deformation and behavior of the structure in different thermal conditions. The boundary conditions for the cylindrical shell are considered as free, clamped and simple. The equations governing the structure of the hybrid cylindrical shell are obtained based on the displacement field and the stress and strain relations in the form of a matrix using the first order shear theory of shells and Hamilton's principle. By using the Generalized Differential Quadrature numerical Method(GDQM), the governing equations of the structure are solved and the effect of composite materials, temperature, cylinder length and geometric dimensions on the natural frequency of the structure has been investigated and analyzed. The numerical results have been compared and verified with the results of the research. The results show that the hybrid shell with the distribution of composite materials and in a specific volume ratio shows better behavior against temperature changes.