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Abstract The contrasting internal luminosity of Uranus and Neptune present a challenge to our understanding of the origin and evolution of these bodies, as well as extra-solar ice giants. The thermal evolution of Neptune is known to be nearly consistent with an entirely fluid interior, but this is not a unique solution, and does not account for the tidal dissipation required by the migration of its moons. We examine a model that has been previously shown to explain the thermal and tidal evolution of Uranus: one that features a growing, frozen core. The core traps heat in the interior, affecting the cooling time scale, and provides a source of tidal dissipation. We review the growing, frozen core model, and the computation of thermal and tidal evolution. We then apply this model to Neptune. We find that the growing frozen core model can account for the observed internal luminosity of Neptune and the migration of its moons, in the form of resonances that were either encountered or avoided in the past. We discuss prospects for observational tests of the growing frozen core model and possible implications for understanding the gas giants.