We studied the power-law heating-rate dependence of superheating for the melting of alpha- and betacrystals of isotactic polypropylene by means of chip-calorimeter, and expanded our parallel observation to higher heating rates by means of molecular simulations. We observed that, at low heating fates, the melting of lamellar crystals after thickened via melting-recrystallization exhibits no power-law-dependent superheating; at medium heating rates, the melting of crystals after thickened via chainsliding diffusion exhibits the power-law-dependent superheating with the power indexes sensitive to chain mobility in the crystals; while at high heating rates, the zero-entropy-production melting of crystals without further thickening maintains the power-law-dependent superheating but with the power indexes uniform at an upper-limit 0.375. We attributed the index 0.375 to a result combining local intramolecular nucleation and global roughening growth at the lateral surface of lamellar crystals, which dominate the kinetics of crystal growth and melting of polymer crystals at high temperatures. (C) 2014 Elsevier Ltd. All rights reserved.