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A thermal current, generated by a temperature gradient between two reservoirs coupled to a carefully designed photonic or (micro-) electromechanical circuit, might induce non-conservative forces that impulse a mechanical degree of freedom to move along a closed trajectory. We show that in the limit of long - but finite - modulation periods, the extracted power and the efficiency of such autonomous motors can be maximized when an appropriately designed spatio-temporal symmetry violation is induced and when the motor operates in the vicinity of exceptional point (EP) degeneracies. These singularities appear in the spectrum of the effective non-Hermitian Hamiltonian that describes the combined circuit-reservoirs system when we judiciously tailor the coupling between them. In the photonic framework, these motors can be propelled by thermal radiation and can be utilized as autonomous self-powered microrobots, or as micro-pumps for microfluidics in biological environments. The same designs can be also implemented with electromechanical elements for harvesting ambient mechanical (or electrical) noise for powering a variety of auxiliary systems.