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 as cooling NSs 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 ~5-6 times smaller than the actual NS radii, again in agreement with observations.