We present Chandra , XMM-Newton , and Swift observations of the quiescent neutron star in the transient low-mass X-ray binary MAXI J0556–332 . Observations of the source made during outburst ( with the Rossi X-ray Timing Explorer ) reveal tracks in its X-ray color–color and hardness–intensity diagrams that closely resemble those of the neutron-star Z sources , suggesting that MAXI J0556–332 had near- or super-Eddington luminosities for a large part of its \sim 16 month outburst . A comparison of these diagrams with those of other Z sources suggests a source distance of 46 \pm 15 kpc . Fits to the quiescent spectra of MAXI J0556–332 with a neutron-star atmosphere model ( with or without a power-law component ) result in distance estimates of 45 \pm 3 kpc , for a neutron-star radius of 10 km and a mass of 1.4 M _ { \odot } . The spectra show the effective surface temperature of the neutron star decreasing monotonically over the first \sim 500 days of quiescence , except for two observations that were likely affected by enhanced low-level accretion . The temperatures we obtain for the fits that include a power-law ( kT _ { eff } ^ { \infty } =184–308 eV ) are much higher than those seen for any other neutron star heated by accretion , while the inferred cooling ( e -folding ) timescale ( \sim 200 days ) is similar to other sources . Fits without a power-law yield higher temperatures ( kT _ { eff } ^ { \infty } =190–336 eV ) and a shorter e -folding time ( \sim 160 days ) . Our results suggest that the heating of the neutron-star crust in MAXI J0556–332 was considerably more efficient than for other systems , possibly indicating additional or more efficient shallow heat sources in its crust .