I will first present the basic ideas behing neutron star cooling modelling. A description of the "minimal cooling paradigm" in is latest version will be followed by a brief look at the alternative scenarios. Since people are interested in it, I will show how the superfluidity/superconductivity fronts are propagating within the star as cooling proceed. Hopefuly I will also present some results about the thermal evolution of a NS undergoing periodic accretion phases, with emphasis on the relaxation of the crust thermal profile.