  Periodic changes in a thermal soft X-ray flux of a rotating neutron star
indicate a non-uniform distribution of the surface temperature. A possible
cause of this phenomenon is a suppression of the heat flux across the magnetic
field lines in a crust and an envelope of magnetized neutron stars. In this
paper we study three-dimensional effects, associated with non-axisymmetric
magnetic fields in neutron stars. We calculate the surface temperature
distribution by solving numerically a three dimensional heat transfer equation
in a magnetized neutron star crust. We adopt an anisotropic (tensorial)
electron thermal conductivity coefficient, which is derived as an analytical
solution of the Boltzmann equation with a Chapman-Enskog method. To calculate
the surface temperature distribution, we construct a local one-dimensional
plane-parallel model ("Ts-Tb"-relationship) of a magnetized neutron star
envelope. We then use it as an outer boundary condition for the
three-dimensional problem in the crust to find the self-consistent solution. To
study possible observational manifestations from anisotropic temperature
distributions we calculate light curves with a composite black-body model. Our
calculations show, that a non-axisymmetric magnetic field distribution can lead
to the irregular non-sinusoidal shape of a pulse profile as well as in some
cases a significant amplification of pulsations of the thermal flux in
comparison to the pure-dipolar magnetic field configurations.
