The neutron star low-mass X-ray binary EXO 0748-676 started a transition from outburst to quiescence in August 2008, after more than 24 years of continuous accretion. The return of the source to quiescence has been monitored extensively by several X-ray observatories. Here, we report on four XMM-Newton observations elapsing a period of more than 19 months that started in November 2008. The X-ray spectra contain a soft thermal component that we fit with a neutron-star atmosphere model. In only the first observation do we find a significant second component above ~3 keV accounting for ~7% of the total flux, which might be indicative of residual accretion. The thermal bolometric flux and the temperature of the neutron star crust decrease steadily by 40% and 10%, respectively, between the first and the fourth observations. At the time of the last observation in June 2010, we obtain a thermal bolometric luminosity of 5.6 × 1033 (d/7.1 kpc)2 erg s-1 and a temperature of the neutron star crust of 109 eV. The cooling curve is consistent with a relatively hot medium-mass neutron star cooling by standard mechanisms. From the spectral fits to a neutron-star atmosphere model, we infer limits to the mass and the radius of the neutron star. We find that to achieve self-consistency between the neutron-star masses derived using the different methods, the value of the distance is constrained to be ≲6 kpc. For this value of the distance, the derived mass and radius contours are consistent with a number of EoSs with nucleons and hyperons.
