Injection molded samples were obtained with a fast evolution of cavity surface temperature technique allowing to keep, for assigned time intervals, the cavity surface temperature at intermediate values between injection and cooling channels temperatures. The surface temperature was changed by activating thin (0.2mm) heating devices layered, inside the mold, very close to the mold surface; the devices were activated by the injection molding machine about 2 s in advance, so as to find the mold surface already heated at the first contact of the polymer inside the cavity. The surface temperature reached a plateau after very short time and the small thickness of the heating device allowed a fast cooling at the power deactivation. Several tests were performed for different levels of the heating power and heating time. The recorded evolutions of surface temperature and of pressure inside the cavity show that, for high heating power and long heating times, the pressure undergoes two pressure steps down: the first as consequence of the cooling from the injection temperature to the heated surface temperature and the second determined by the cooling to the mold temperature due to the heating deactivation. The polymer shrinkage due to crystallization contributes to the amount of each of the two pressure steps. For small heating times the two cooling steps collapse into a single one. The effects of temperature, pressure and flow on relaxation times, nucleation density, spherulitic growth rate, as well as the interrelation among these quantities were experimentally analyzed and included into an overall injection moulding simulation model for the iPP grade developed in the UNISA code. The simulation results of the UNISA code (modified to the purpose of accounting of the surface heating) favorably compare with the experimental results of temperature evolutions. Also simulation results of pressure evolutions reproduce main features shown by the experimental results.