Several amorphous narrow molecular weight fractions of poly(aryl ether ether ketone) or PEEK have been heated from below their glass transition temperature to above their final melting point. The semicrystalline morphology induced by cold crystallization and its thermal evolution are studied by time-resolved simultaneous small-angle X-ray scattering (SAXS), wide-angle X-ray diffraction, and differential scanning calorimetry. The long period and the crystalline and the amorphous thicknesses are computed from the correlation function of the SAXS curves. The evolution of the structural parameters of the various semicrystalline samples can be reconciled with the existence of a single distribution of lamellae which undergoes reorganization during the continuous heating. The reorganization process as well as the semicrystalline morphology depends on the molecular weight of the fractions. The amorphous thickness strongly increases with the molecular weight while the thermal evolution of the thickness of the crystalline layers is similar for all fractions. These experimental results support the view that the larger degree of entanglements of the high molecular weight samples impedes the reorganization mechanism with the consequence that the apparent melting temperature decreases with increasing average molecular weight.