Abstract The study of transiently accreting neutron stars provides a powerful means to elucidate the properties of neutron star crusts. We present extensive numerical simulations of the evolution of the neutron star in the transient low-mass X-ray binary MAXI J0556–332. We model nearly 20 observations obtained during the quiescence phases after four different outbursts of the source in the past decade, considering the heating of the star during accretion by the deep crustal heating mechanism complemented by some shallow heating source. We show that cooling data are consistent with a single source of shallow heating acting during the last three outbursts, while a very different and powerful energy source is required to explain the extremely high effective temperature of the neutron star, ∼350 eV, when it exited the first observed outburst. We propose that a gigantic thermonuclear explosion, a “hyperburst” from unstable burning of neutron-rich isotopes of oxygen or neon, occurred a few weeks before the end of the first outburst, releasing ∼10⁴⁴ ergs at densities of the order of 10¹¹ g cm⁻³. This would be the first observation of a hyperburst, and these would be extremely rare events, as the buildup of the exploding layer requires about a millennium of accretion history. Despite its large energy output, the hyperburst did not produce, due to its depth, any noticeable increase in luminosity during the accretion phase and is only identifiable by its imprint on the later cooling of the neutron star.