  Recent ROSAT measurements show that the x-ray emission from isolated neutron
stars is modulated at the stellar rotation period. To interpret these
measurements, one needs precise calculations of the heat transfer through the
thin insulating envelopes of neutron stars. We present nearly analytic models
of the thermal structure of the envelopes of ultramagnetized neutron stars.
Specifically, we examine the limit in which only the ground Landau level is
filled. We use the models to estimate the amplitude of modulation expected from
non-uniformities in the surface temperatures of strongly magnetized neutron
stars. In addition, we estimate cooling rates for stars with fields $B \sim
10^{15}-10^{16}$ G which are relevant to models that invoke ``magnetars'' to
account for soft $\gamma$-ray emission from some repeating sources.
