Oriented fibers of atactic Polyacrylonitrile (PAN) show a diffraction pattern consisting of just two equatorial peaks. The plot of d-spacing vs. temperature shows a linear increase up to about 85-100°C, followed by another linear region with augmented slope. This increase in slope occurs at a temperature that coincides with a glass transition (denoted TgII). It could not be explained previously, as with the classical two- phase model of polymers (amorphous + crystalline domains), there should be no change at a glass-transition because the amorphous phase with which a Tg is normally associated gives no X-ray peaks. In this work, we are able to explain why there can be a change in slope in the d-spacings of the ordered phase at a glass transition. This is because the ordered phase in PAN is not crystalline, but is a mesophase glass, and the transition is from a mesophase glass to a mesophase melt.