The increment of heat capacity at the glass transition for semi-crystalline poly(ethylene terephthalate) (PET) observed by temperature-modulated differential scanning calorimetry (TMDSC) shows significant deviations from a simple crystalline/amorphous two-phase model. Introduction of a rigid amorphous fraction, which is non-crystalline but which also does not participate in the normal glass transition, allows a much better description of the transition behaviour in semi-crystalline PET. Certain questions arise such as what is the rigid amorphous fraction and over what temperature range do these rigid amorphous segments devitrify? These TMDSC results show that the rigid amorphous component may be treated as an interphase between amorphous and crystalline phases. This interphase does not exhibit a separate glass transition temperature at temperatures above the normal Tg. The suggestion is made that the glass transition of the rigid amorphous component occurs continually between the glass transition temperature of the amorphous phase and up to about 135C for this particular sample of PET.