  We examine properties of thermal radiation emitted by strongly magnetized
neutron stars (NSs). In particular, we show that the pulsation amplitudes of
the energy-integrated flux are an increasing function of the absorption column
density to the source. This is especially important for the interpretation of
the Anomalous $X$-ray Pulsars (AXPs) as cooling neutron stars with high
magnetic fields. We show that the high-pulsation amplitudes observed in these
objects are consistent with cooling models, if the large amount of absorption
to these sources is taken into account. We also show that cooling models imply
inferred radii of the emitting regions on the order of $\sim 5-6$ times smaller
than the actual NS radii, again in agreement with observations.
