We describe the cooling theory of neutron stars which are a few tens of years old. Their cooling is very different from the cooling of older stars that is well studied in the literature. The cooling of a young star is sensitive to the physics of its inner crust and even to the thermal conductivity of its core that is never important at later stages. A non-detection of a neutron star in the Supernova Remnant 1987A does not contradict the assumption that the star was born there. It can still be hidden in a dense center of the supernova remnant. If not hidden, it should have a low thermal luminosity (lower than about 10³⁴ erg/s) and a short internal relaxation time (shorter than 13 years). It is possible if the star undergoes powerful neutrino cooling (e.g., by the direct Urca process) and has a thin crust with strong superfluidity of free neutrons and/or anomalously high thermal conductivity.

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