  Superbursts are very energetic Type I X-ray bursts discovered in recent years
by long term monitoring of X-ray bursters, and believed to be due to unstable
ignition of carbon in the deep ocean of the neutron star. In this Letter, we
follow the thermal evolution of the surface layers as they cool following the
burst. The resulting lightcurves agree very well with observations for layer
masses and energy releases in the range expected from ignition calculations. At
late times, the cooling flux from the layer decays as a power law in time,
giving timescales for quenching of normal Type I bursting of weeks, in good
agreement with observational limits. We show that simultaneous modelling of
superburst lightcurves and quenching times promises to constrain both the
thickness of the fuel layer and the energy deposited.
