discussed cooling of strange stars and neutron stars with quark cores. A comprehensive review is given in [@pgw06].

Connections
===========

With the spectacular progress of neutron star observations, cooling problem becomes more connected to other aspects of neutron star physics. First, cooling of isolated neutron stars is closely related to deep crustal heating of transiently accreting neutron stars in soft X-ray transients (SXTs). The matter accreted on a neutron star becomes eventually compressed by the weight of newly accreted material and sinks thus into the crust. Sinking into the deep crust is accompanied by nuclear transformations [@hz90; @hz03; @guptaetal07; @hz07] and associated heating of the entire star ($1.5-2$ MeV per one accreted nucleon). This deep crustal heating can keep thermally inertial stars warm [@bbr98] even in quiescent states of SXTs when accretion is switched off. It is likely responsible for thermal emission observed from some SXTs in quiescent states (e.g., Refs. [@heinke07; @jonker07]).

One can distinguish two heating regimes. As a rule, accretion episodes are not too long (weeks-months) and do not violate isothermality of internal layers. These stars reach thermal quasiequilibrium determined by the mass accretion rates $\langle \dot{M} \rangle$ averaged over their global thermal relaxation time ($\sim 100-1000$ 