Evidence for Heating of Neutron Stars by Magnetic Field Decay
  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. 
J.A. Pons, B. Link, J.A. Miralles, and U. Geppert