We present two-dimensional simulations for the cooling of neutron stars with strong magnetic fields (B > 1e13 Gauss). We study how the cooling curves are influenced by magnetic field decay. We show that the Joule heating effects are very large and in some cases control the thermal evolution. We characterize the temperature anisotropy induced by the magnetic field and predict the surface temperature distribution for the early and late stages of the evolution of isolated neutron stars, comparing our results with available observational data of isolated neutron stars.
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