  Recently launched x-ray telescopes have discovered several candidate isolated
neutron stars. The thermal radiation from these objects may potentially
constrain our understanding of nuclear physics in a realm inaccessible to
terrestrial experiments. To translate the observed fluxes from neutron stars
into constraints, one needs precise calculations of the heat transfer through
the thin insulating envelopes of neutron stars. We describe models of the
thermal structure of the envelopes of neutron stars with magnetic fields up to
10^{14} G. Unlike earlier work, we infer the properties of envelope models in
two dimensions and precisely account for the quantization of the electron phase
space. Both dipole and uniformly magnetized envelopes are considered.
