The structure and the thermal response of polyethylene terephthalate (PET) fibers, melt‐spun at speeds of 3 to 6 km/min, are investigated in the temperature region 0–200'C. Differential scanning calorimetry thermograms, and radial distribution functions from wide‐angle x‐ray scattering are used. Interpretation of multiple glass transition and crystallization peaks and of the range of structural coherence is interpreted in terms of a nonhomogeneous molecular arrangement for fibers melt‐spun at intermediate spinning speeds. A three‐phase model of the molecular structure of these fibers is used to explain the results. An important feature of the model is the existence of a threadlike, interconnected, highly oriented noncrystalline phase, coexisting with a more unoriented amorphous phase. The model can qualitatively explain a number of experimental observations. Copyright © 1990 John Wiley & Sons, Inc.