  We present models of temperature distribution in the crust of a neutron star
in the presence of a strong toroidal component superposed to the poloidal
component of the magnetic field. The presence of such a toroidal field hinders
heat flow toward the surface in a large part of the crust. As a result, the
neutron star surface presents two warm regions surrounded by extended cold
regions and has a thermal luminosity much lower than in the case the magnetic
field is purely poloidal. We apply these models to calculate the thermal
evolution of such neutron stars and show that the lowered photon luminosity
naturally extends their life-time as detectable thermal X-ray sources.
