In polymer processing as fibre spinning, injection moulding, film casting and so on, the forming phase of the melt is followed by its solidification due to cooling. This implies the crystallization of the polymer during the processing. Typically, crystallites are formed and an ordered structure can be detected, if the cooling rate is not too high. As a consequence, during processing the rheological response of the material significantly changes from a liquid-like to a solid-like behaviour. The knowledge of the mechanical response of the material during crystallization is therefore of seminal importance for process control and modelling. We here focus on a random copolymer, the Ethylene vinyl acetate (EVA), made of ethylene and varying amounts of vinyl acetate that interfere with poly-ethylene chain packing reducing the crystallinity, improving the transparency and lowering the melting temperature. This allows studying the crystallization kinetics at relatively low temperatures so to avoid all the experimental issues related to thermal degradation. The crystallization process is rheologically studied in non-isothermal conditions and the frequency spectra are measured at different temperatures to investigate the viscoelasticity of EVA during the change of phase. Coupling the crystallization kinetics and the viscoelastic spectra at different temperatures, i.e. at different degree of crystallinity, we determine two independent shift factors, one for the time-crystallinity shift, the other for the time-temperature shift, so to propose a new time-temperature-crystallinity superposition to reconcile all the data on a single master curve. In this way, the experimentally observable frequency range has been widen significantly so to detect all the relaxation times of the material from the shortest to the largest ones.