Although the thermal buckling problem of functionally gradient material (FGM) cylindrical shells has been investigated for many years, its theoretical solution is rarely reported when considering the material properties varying with temperature, and the existing commercial software also cannot directly solve the critical temperature rise of thermal buckling. Therefore, the theoretical solution of critical temperature rise was first derived for the FGM-coated cylindrical shell with temperature-dependent material properties based on the Donnell thin shell theory. And then, a stepped layer discrete finite element (FE) model was developed by integrating the bisection method into a user subroutine to calculate the critical temperature rise. The results show that the theoretical solutions are in good agreement with the numerical ones, and find out the temperature has a relatively large negative effect on the thermal buckling resistance of the FGM-coated cylindrical shell. Finally, the influence factors on the critical temperature rise were discussed in detail, and some suggestions have been formed to improve the calculation accuracy. This work not only provides a theoretical calculation formula but also develops an FE numerical method to calculate the critical temperature rise of the FGM-coated cylindrical shell, which will help the engineers to design the FGM-related structures easily.