Thermal diffusivity (alpha) of poly(ethylene terephthalate) (PET) and poly(ethylene naphthalate) (PEN) was measured by an AC joule heating technique as a function of temperature from the solid to the liquid state; alpha changed drastically at the glass transition and at crystallization. In a heating run on the quenched sample, an abrupt increase of alpha immediately after the glass transition was observed, which corresponded to cold crystallization. The relationship between glass transition temperature (T-g) and the change ratio of alpha at the glass transition (Delta alpha/alpha) of PET and PEN deviated from that of amorphous polymers. A biaxial stretching of PET and PEN resulted in a lowering of alpha vertical to the stretched direction. An upward shift of T-g and a reduced drop in a at the glass transition (Delta alpha) was also observed.