  We continue the study of the effects of a strong magnetic field on the
temperature distribution in the crust of a magnetized neutron star (NS) and its
impact on the observable surface temperature. Extending the approach initiated
in Geppert et al.(2004), we consider more complex and, hence, more realistic,
magnetic field structures but still restrict ourselves to axisymmetric
configurations. We put special emphasis on the heat blanketing effect of a
toroidal field component. We show that asymmetric temperature distributions can
occur and a crustal field consisting of dipolar poloidal and toroidal
components will cause one polar spot to be larger than the opposing one. These
two warm regions can be separated by an extended cold equatorial belt. We
present an internal magnetic field structure which can explain both the X-ray
and optical spectra of the isolated NS RXJ 1856-3754. We investigate the
effects of the resulting surface temperature profiles on the observable
lightcurve which an isolated thermally emitting NS would produce for different
field geometries. The lightcurves will be both qualitatively (deviations from
sinusoidal shape) and quantitatively (larger pulsed fraction for the same
observational geometry) different from those of a NS with an isothermal crust.
This opens the possibility to determine the interna} magnetic field strengths
and structures in NSs by modeling their X-ray lightcurves and spectra. The
striking similarities of our model calculations with the observed spectra and
pulse profiles of isolated thermally emitting NSs is an indication for the
existence of strong magnetic field components maintained by crustal currents.
