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An accretion outburst in an X-ray transient deposits material onto theneutron star primary; this accumulation of matter induces reactions in theneutron star's crust. During the accretion outburst these reactions heat thecrust out of thermal equilibrium with the core. When accretion halts, the crustcools to its long-term equilibrium temperature on observable timescales. Herewe examine the accreting neutron star transient MAXI J0556-332, which is thehottest transient, at the start of quiescence, observed to date. Models of thequiescent light curve require a large deposition of heat in the shallow outercrust from an unknown source. The additional heat injected is $\approx4\textrm{-}10\,\mathrm{MeV}$ per accreted nucleon; when the observed decline inaccretion rate at the end of the outburst is accounted for, the requiredheating increases to $\approx 6\textrm{-}16\,\mathrm{MeV}$. This shallowheating is still required to fit the lightcurve even after taking into accounta second accretion episode, uncertainties in distance, and different surfacegravities. The amount of shallow heating is larger than that inferred for otherneutron star transients and is larger than can be supplied by nuclear reactionsor compositionally driven convection; but it is consistent with storedmechanical energy in the accretion disk. The high crust temperature ($T_b\gtrsim 10^{9} \, {\rm K}$) makes its cooling behavior in quiescence largelyindependent of the crust composition and envelope properties, so that futureobservations will probe the gravity of the source. Fits to the lightcurvedisfavor the presence of Urca cooling pairs in the crust.

A strong shallow heat source in the accreting neutron star MAXI J0556-332