  We study the efficiency of Joule heating in the crustal layers of young
neutron stars. It is shown that dissipation of the magnetic field is highly
inhomogeneous in the crust with much faster dissipation in relatively low
density layers. In young neutron stars, the rate of Joule heating in the crust
can exceed the standard luminosity of non-magnetic star and can even be
comparable to the luminosity of magnetars. The results of calculations are
compared with the available observational data. We argue that the crustal field
model can well account for the data on the surface temperature and magnetic
field of young neutron stars.
