Melt-crystallization of poly (butylene 2,6-naphthalate) (PBN) at temperatures lower than about 160 degrees C follows Ostwald's rule of stages, leading first to formation of a transient smectic liquid crystalline phase (LC) which then may convert in a second step into crystals, controlled by kinetics. In the present work, the PBN melt was cooled at different rates in a fast scanning chip calorimeter to below the glass transition temperature, to obtain different structural states before analysis of the cold-crystallization behavior on heating. It was found that heating of fully amorphous PBN at 1000 K/s leads to a similar two-step crystallization process as on cooling the quiescent melt, with LC-formation occurring slightly above T-g and their transformation into crystals at their stability limit close to 200 degrees C. In-situ polarized-light optical microscopy provided information that the transition of the LC-phase into crystals on slow heating is not connected with a change of the micrometer-scale superstructure, as the recently found Schlieren texture remains unchanged.