the SQUID degrees of freedom and show that it gives rise to a three-body interaction Hamiltonian with the cavity modes. By considering only two interacting modes from the cavities we show that the device can function as an autonomous cooler where the SQUID can be used as a work source to cool down the cavity modes. Moreover, this setup allows for coupling to all modes existing inside the cavities, and we show that by adding two other extra modes to the interaction with the SQUID the cooling effect can be enhanced.