Method of making multilayer preforms which resist delamination and in a reduced cycle time. A first array of preforms are molded onto a first array of cores in an associated array of mold cavities, the cores and preforms are removed from the mold cavities as soon as possible without significant physical preform deformation, and the preforms are then cooled on the cores while a second array of cores is positioned in the mold cavities. Cooling on the cores prevents delamination of the preform layers and reduces the in-mold cooling time. Providing multiple sets of cores on a rotating turret further reduces the cycle time compared to the prior art use of robotic cooling tubes.