To investigate the contributions of polymer relaxation phenomena to the mechanism of disperse dye adsorption on poly(ethylene terephthalate) fibres, a commercial grade dye was applied to poly(ethylene terephthalate) fabric at temperatures between 30°C and 130°C. Three regions of temperature‐dependent dyeing behaviour were identified, in which the promotional effect imparted by increasing dyeing temperature varied, depending on whether dyeing had been carried out at temperatures that were below, within or above the polymer's glass transition temperature, Tg, namely < 65°C, between 65°C and 110°C and between 110°C and 130°C, respectively. When experimentally determined colour strength data points (log 1/fk) were fitted to plots of polymer structural relaxation (log aT) calculated using the Williams, Landel and Ferry equation as a function of (T − Tg), three different levels of correspondence were achieved which paralleled the observed three regions of temperature‐dependent dye uptake. The adsorption of the commercial disperse dye on the poly(ethylene terephthalate) fibre therefore concurs with the free volume model of dye diffusion insofar as the diffusional behaviour of the dye is related to the relaxation time of the molecular motions occurring within the poly(ethylene terephthalate) polymer. The finding that the poly(ethylene terephthalate) substrate's glass transition extends over a broad range of temperature upto ~110°C explains why elevated dyeing temperatures in the region of 130/140°C must be used in High Temperature dyeing processes, and also, why ~75% of uptake of the commercial disperse dye on the poly(ethylene terephthalate) fabric occurs over the very narrow 20‐30°C critical temperature range between 110 and 130°C/140°C.