PAN fibres, consisting of poly[acrylonitrile-co-(methyl acrylate)], were oxidatively heat treated at low temperatures (up to 180 • C), during which the basic macromolecular backbone was not cyclized. The change of length of the fibres was determined under various treatment conditions (ie temperature, time, stress applied). Prolonged heat treatment resulted in lower tensile strength of the fibres. The pristine and treated fibres were characterized by Fourier-transform infrared (FTIR), NMR and UV-visible spectroscopy and by TGA, and the results were used for representing the different regions according to chemical aspects in a plot of temperature versus time; this is very important for the whole treatment process. A shrinkage model was proposed, having both scientific and technical importance. The change in activation volume of shrinkage of fibres with temperature, calculated from this model, is indicative of the physical transitions taking place at the molecular scale.