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Periodic changes in a thermal soft X-ray flux of a rotating neutron starindicate a non-uniform distribution of the surface temperature. A possiblecause of this phenomenon is a suppression of the heat flux across the magneticfield lines in a crust and an envelope of magnetized neutron stars. In thispaper we study three-dimensional effects, associated with non-axisymmetricmagnetic fields in neutron stars. We calculate the surface temperaturedistribution by solving numerically a three dimensional heat transfer equationin a magnetized neutron star crust. We adopt an anisotropic (tensorial)electron thermal conductivity coefficient, which is derived as an analyticalsolution of the Boltzmann equation with a Chapman-Enskog method. To calculatethe surface temperature distribution, we construct a local one-dimensionalplane-parallel model ("Ts-Tb"-relationship) of a magnetized neutron starenvelope. We then use it as an outer boundary condition for thethree-dimensional problem in the crust to find the self-consistent solution. Tostudy possible observational manifestations from anisotropic temperaturedistributions we calculate light curves with a composite black-body model. Ourcalculations show, that a non-axisymmetric magnetic field distribution can leadto the irregular non-sinusoidal shape of a pulse profile as well as in somecases a significant amplification of pulsations of the thermal flux incomparison to the pure-dipolar magnetic field configurations.

3D numerical study of an anisotropic heat transfer in outer layers of magnetized neutron stars