  Using recently calculated analytic models for the thermal structure of
ultramagnetized neutron stars, we estimate the thermal fluxes from young
($t\sim 1000$ yr) ultramagnetized ($B \sim 10^{15}$ G) cooling neutron stars.
We find that the pulsed X-ray emission from objects such as 1E 1841-045 and 1E
2259+586 as well as many soft-gamma repeaters can be explained by photon
cooling if the neutron star possesses a thin insulating envelope of matter of
low atomic weight at densities $\rho < 10^{7}-10^{8}$ g/cm$^3$. The total mass
of this insulating layer is $M \sim 10^{-11}-10^{-8} M_\odot$.
