Exploring the limits of the microscopic reversibility principle, we investigated the interplay between thermal and electron tunneling excitations for the unidirectional rotation of a molecule-rotor on the Au(111) surface. We identified a range of moderate voltages and temperatures where heating the surface enhances the unidirectional rotational rate of a chemisorbed DMNI-P rotor. At higher voltage, inelastic tunneling effects dominate while at higher temperature the process becomes stochastic. At each electron transfer event during tunneling, the quantum mixing of ground and excited electronic states brings part of the surface thermal energy in the excited electronic states of the molecule-rotor. Thermal energy contributes therefore to the semi-classical unidirectional rotation without contradicting the microscopic reversibility principle.