  Neutron stars cool down during their lifetime through the combination of
neutrino emission from the interior and photon cooling from the surface.
Strongly magnetised neutron stars, called magnetars, are no exception, but the
effect of their strong fields adds further complexities to the cooling theory.
Besides other factors, modelling the outermost hundred meters (the envelope)
plays a crucial role in predicting their surface temperatures. In this letter,
we revisit the influence of envelopes on the cooling properties of neutron
stars, with special focus on the critical effects of the magnetic field. We
explore how our understanding of the relation between the internal and surface
temperatures has evolved over the past two decades, and how different
assumptions about the neutron star envelope and field topology lead to
radically different conclusions on the surface temperature and its cooling with
age. In particular, we find that relatively old magnetars with core-threading
magnetic fields are actually much cooler than a rotation-powered pulsar of the
same age. This is at variance with what is typically observed in
crustal-confined models. Our results have important implications for the
estimates of the X-ray luminosities of aged magnetars, and the subsequent
population study of the different neutron star classes.
