Joule heating and the thermal evolution of old neutron stars

We consider Joule heating caused by dissipation of the magnetic held in the neutron star crust. This mechanism may be efficient in maintaining a relat ively high surface temperature in very old neutron stars. Calculations of t he thermal evolution show that, at the late evolutionary stage (t greater t han or equal to 10 Myr), the luminosity of the neutron star is approximatel y equal to the energy released due to the held dissipation and is practical ly independent of the atmosphere models. At this stage, the surface tempera ture can be of the order of 3 x 10(4)-10(5) K. Joule heating can maintain t his high temperature for an extremely long time (greater than or equal to 1 00 Myr), comparable with the decay time of the magnetic field.