We consider Joule heating caused by dissipation of the magnetic field in the
neutron star crust. This mechanism may be efficient in maintaining a relatively
high surface temperature in very old neutron stars. Calculations of the thermal
evolution show that, at the late evolutionary stage (t≥10 Myr), the
luminosity of the neutron star is approximately equal to the energy released
due to the field dissipation and is practically independent of the atmosphere
models. At this stage, the surface temperature can be of the order of 3×104−105K. Joule heating can maintain this high temperature during
extremely long time (≥100 Myr), comparable with the decay time of the
magnetic field.Comment: 13 pages (5 figures in the text). Accepted for publication in The
Astrophysical Journa