In late 2008 , the quasi-persistent neutron star X-ray transient and eclipsing binary EXO 0748–676 started a transition from outburst to quiescence , after it had been actively accreting for more than 24 years . In a previous work , we discussed Chandra and Swift observations obtained during the first five months after this transition . Here , we report on further X-ray observations of EXO 0748–676 , extending the quiescent monitoring to 1.6 years . Chandra and XMM-Newton data reveal quiescent X-ray spectra composed of a soft , thermal component that is well-fitted by a neutron star atmosphere model . An additional hard powerlaw tail is detected that changes non-monotonically over time , contributing between 4 and 20 percent to the total unabsorbed 0.5–10 keV flux . The combined set of Chandra , XMM-Newton and Swift data reveals that the thermal bolometric luminosity fades from \sim 1 \times 10 ^ { 34 } to 6 \times 10 ^ { 33 } ~ { } ( \mathrm { D / 7.4 ~ { } kpc } ) ^ { 2 } ~ { } \mathrm { erg~ { } s } ^ { -1 } , whereas the inferred neutron star effective temperature decreases from \sim 124 to 109 eV . We interpret the observed decay as cooling of the neutron star crust and show that the fractional quiescent temperature change of EXO 0748–676 is markedly smaller than observed for three other neutron star X-ray binaries that underwent prolonged accretion outbursts .