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The thermal structure of neutron stars with magnetized envelopes is studiedusing modern physics input. The relation between the internal (T_i) and localsurface temperatures is calculated and fitted by analytic expressions formagnetic field strengths B from 0 to 10^{16} G and arbitrary inclination of thefield lines to the surface. The luminosity of a neutron star with dipolemagnetic field is calculated and fitted as a function of B, T_i, stellar massand radius. In addition, we simulate cooling of neutron stars with magnetizedenvelopes. In particular, we analyse ultramagnetized envelopes of magnetars andalso the effects of the magnetic field of the Vela pulsar on the determinationof critical temperatures of neutron and proton superfluids in its core.Comment: 14 pages, 1 table, 11 figures, LaTeX2e using aa.cls (included) and  epsf.sty. Accepted by A&A. Proof-stage version: minor text corrections and  one correction of an in-line formul

Thermal structure and cooling of neutron stars with magnetized envelopes