Cooling of neutron stars with dipole magnetic fields is simulated usin
g a realistic model-like anisotropic surface temperature distribution
produced by magnetic fields. Suppression of the electron thermal condu
ctivity of outer stellar layers across the field increases thermal iso
lation of these layers near the magnetic equator. Enhancement of the r
adiative and longitudinal electron thermal conductivities in quantizin
g magnetic fields reduces thermal isolation near the magnetic poles. T
he equatorial increase of the isolation is pronounced for B greater th
an or similar to 10(10) G, while the polar decrease - for B greater th
an or similar to 10(12) G. The effects compensate partly each other, a
nd the actual influence of the magnetic fields on the cooling is weake
r than predicted by the traditional theories where the equatorial effe
cts have been neglected.