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We show the existence of a strong trend between neutron star surfacetemperature and the dipolar component of the magnetic field extending throughthree orders of field magnitude, a range that includes magnetars, radio-quietisolated neutron stars, and many ordinary radio pulsars. We suggest that thistrend can be explained by the decay of currents in the crust over a time scaleof few Myr. We estimate the minimum temperature that a NS with a given magneticfield can reach in this interpretation.Comment: 4 pages, 1 figures, version accepted for publication in Phys. Rev.  Let

Evidence for Heating of Neutron Stars by Magnetic-Field Decay