Aims. In magnetized neutron star envelopes, the heat transport accross the magnetic field is realized by phonons. We calculate the phonon thermal conductivity in neutron star crusts, including phonon-phonon and phonon-electron scattering.

Methods. Thermal conduction by phonons is calculated using variational solutions of the transport equation. The phase space integrals are performed using the Monte-Carlo method.

Results. Numerical results are approximated by analytical fitting expressions, valid for 10⁵ K T <∼ 10⁸ K and 10⁵ g cm^-3 <∼ ρ <∼ 10¹³ g cm^-3.

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