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We discuss the thermalisation process of the neutron stars crust described bysolving the heat transport equation with a microscopic input for the specificheat of baryonic matter. The heat equation is solved with initial conditionsspecific to a rapid cooling of the core. To calculate the specific heat ofinner crust baryonic matter, i.e., nuclear clusters and unbound neutrons, weuse the quasiparticle spectrum provided by the Hartree-Fock-Bogoliubov approachat finite temperature. In this framework we analyse the dependence of the crustthermalisation on pairing properties and on cluster structure of inner crustmatter. It is shown that the pairing correlations reduce the crustthermalisation time by a very large fraction. The calculations show also thatthe nuclear clusters have a non-negligible influence on the time evolution ofthe surface temperature of the neutron star.

Thermalisation time and specific heat of neutron stars crust