In this research, we investigated the use of concurrent multiscale topology optimization to design additively manufacturable lightweight porous compliant mechanisms that enable harnessing heat energy as the energy source to perform mechanical actions. By establishing two independent dimensionless representations of the design problem, i.e., macro and microscale domains, a concurrent multiscale topology optimization framework is implemented, and the effective properties of the microscale (i.e., elastic and heat conductivity tensors, as well as the thermal expansion coefficient) are calculated and used as the thermo-elastic modeling effective properties of the macroscale. For heat transfer physics, heat transport in solids, as well as heat convection, are simultaneously considered in this study. Sensitivity analysis on the suggested concurrent optimization scheme was derived to address the macro and microstructure coupling as well as the thermo-elastic physics coupling. Several numerical cases are studied with single and multiple microstructure systems. To investigate the macrostructure dependency on the microstructure systems, a study was performed for multiple microstructure subsystems. Incorporating several microstructures into a single macro design domain increased design freedom and improved the performance-to-weight ratio. Furthermore, and for achieving good additive manufacturability we investigated the connectivity of the multi-microstructure optimization and implement boundary competitivity technique to attain fully connected design for attaining good additive manufacturability.