In this study, the multi-objective optimal design of functionally graded material flywheels is obtained using the non-dominated sorting genetic algorithm-II. The variations in temperature along the flywheel radius due to the operating conditions and environmental changes are taken into consideration in design optimization. Variations in the elastic and thermal properties of materials with temperature are taken into consideration for the first time, to the best of the authors' knowledge. The thermoelastic equations of motion and the heat equation are derived and then solved by the generalized differential quadrature method. Results for temperature variation, radial displacement and von Mises stress are compared with the results of finite element analysis, and very good agreement is observed. Designs with optimal cross-sectional geometry and material distribution that give minimum mass and maximum kinetic energy are obtained.