A nanoelectromechanical weak link composed of a carbon nanotube suspended between two normal electrodes in a gap between two superconducting leads is considered. The nanotube is treated as a movable single level quantum dot in which the position-dependent superconducting order parameter is induced due to the Cooper pair tunneling. We show that electron tunneling processes significantly affect the state of the mechanical subsystem. We found that at a given direction of the applied voltage between the electrodes, the stationary state of the mechanical subsystem has a Boltzmann form with an effective temperature dependent on the parameters of the device. As this takes place, the effective temperature can reach significantly small values (cooling effect). We also demonstrate that nanotube fluctuations strongly affect the dc current through the system. The latter can be used to probe the predicted effects in an experiment. Published under an exclusive license by AIP Publishing.