When crosslinked closed cell polyolefin foams are under a temperature above the melting point of the base polymer, a reduction of their size is expected due to the gas diffusion out of the foam. However, some kinds of crosslinked closed cell polyolefin foams present one direction (thickness direction) in which the foam size increases during the first minutes of the thermal treatment. The thickness of the foams after the thermal treatment can be higher than the thickness of the original foams. An experimental study is presented on the thickness increase, as well as on the changes in the dimensions and the properties of foams with different densities, which were obtained from different foaming processes and made of different base polymers, as a function of the treatment temperature and the treatment time. This investigation sought to discover the physics mechanisms that control the anomalous thickness increase. The experimental results show that the thickness increase of these materials is related to the anisotropic cellular structure of the original foams.