  The impact of strong magnetic fields B>10e13 G on the thermal evolution of
neutron stars is investigated, including crustal heating by magnetic field
decay. For this purpose, we perform 2D cooling simulations with anisotropic
thermal conductivity considering all relevant neutrino emission processes for
realistic neutron stars. The standard cooling models of neutron stars are
called into question by showing that the magnetic field has relevant (and in
many cases dominant) effects on the thermal evolution. The presence of the
magnetic field significantly affects the thermal surface distribution and the
cooling history of these objects during both, the early neutrino cooling era
and the late photon cooling era. The minimal cooling scenario is thus more
complex than generally assumed. A consistent magneto-thermal evolution of
magnetized neutron stars is needed to explain the observations.
