  We show the existence of a strong trend between neutron star surface
temperature and the dipolar component of the magnetic field extending through
three orders of field magnitude, a range that includes magnetars, radio-quiet
isolated neutron stars, and many ordinary radio pulsars. We suggest that this
trend can be explained by the decay of currents in the crust over a time scale
of few Myr. We estimate the minimum temperature that a NS with a given magnetic
field can reach in this interpretation.
