A precise control and understanding of the magnetization dynamics of nanostructures is an important topic in applied nanosciences. Herein, we perform such control by annealing crystalline (Co/core)–(Pt/shell) nanoparticles. Using electron tomography, temperature dependent electron microscopy and time-resolved magneto-optics, we establish a clear correlation between the magnetization dynamics and the crystalline structure of the nanoparticles. For a mild laser annealing (370 K) the Co–Pt nanoparticles keep their core–shell structure and remain superparamagnetic with a blocking temperature TB = 66 K. Their time-resolved reflectivity shows that they are locally organized into a supra-crystalline ordered layer in the region of the laser spot. In contrast, a thermal annealing at higher temperatures (up to 700 K) modifies the structure of the individual nanoparticles into a CoPt crystalline ferromagnetic phase, with TB,anneal= 347 K. Correspondingly, the magneto-crystalline anisotropy of the annealed CoPt nanoparticles increases and their magnetization dynamics displays a motion of precession, characteristic of ferromagnetic nanostructures and which is absent in the superparamagnetic Co–Pt core–shells.