  We model the temperature distribution at the surface of a magnetized neutron
star and study the effects on the observable X-ray spectra and light curves,
taking fully into account gravitational lensing. Only dipolar fields are
considered here. General features are studied and compared with the ROSAT data
from the pulsars 0833-45 (Vela), 0656+14, 0630+178 (Geminga), and 1055-52.
  The composite blackbody spectra obtained are not very different from a black-
body spectrum at the star's effective temperature: temperature estimates using
single temperature models are practically equivalent to composite model
results.
  Gravitational lensing strongly suppresses the light curve pulsations: this
may be a new tool to constrain the size of neutron stars.
  Dipolar surface fields yield many features somewhat similar to the observed
ones but are not sufficient for an accurate description.
  The pulsed fractions obtained in all our models increase with photon energy:
the strong decrease observed in Geminga at energies 0.3 - 0.5 keV is definitely
a genuine effect of the atmospheric magnetic field on the locally emitted
spectrum in contradistinction to the magnetic effects on the surface
temperature.
  A complete model will have to consider complex surface field structures and
include effects of the atmospheric magnetic field on the emitted spectrum.
