We present the first large-scale molecular dynamics simulations of hexane on graphite that completely reproduce all experimental features of the melting transition. The canonical ensemble simulations required and used the most realistic model of the system: (i) a fully atomistic representation of hexane; (ii) an explicit site-by-site interaction with carbon atoms in graphite; (iii) the CHARMM force field with carefully chosen adjustable parameters of nonbonded interaction, and (iv) numerous >= 100 ns runs, requiring a total computation time of ca. 10 CPU years. The exhaustive studies have allowed us to determine the mechanism of the transition: proliferation of small domains through molecular reorientation within lamellae and without perturbation of the overall adsorbed film structure. At temperatures greater than that of melting, the system exhibits dynamically reorienting domains whose orientations reflect the graphite substrate's symmetry and whose size decrease with increasing temperature.