A compliant mechanism is a mechanism that produces its motion by the flexibility of some or all of its members when input force or thermal load is applied. Whereas the topology optimizations based on homogenization and SIMP parameterization have been successfully applied for compliant mechanism design, ESO approach has been hardly considered yet for the optimization of these types of systems. In this paper, traditional ESO method is adopted to achieve the optimum design of a compliant mechanism for thermal load, since AESO method cannot consider the effect of both heat conduction and convection. Sensitivity number, a criterion for element removal in traditional ESO, was newly defined for input thermal loading. The procedure has been tested in numerical applications and compared with the results obtained by other methods to validate these approaches.