Crystalline-to-rotator phase transitions have been widely studied in bulk hydrocarbons, in particular in normal alkanes. But few studies of these transitions deal with molecularly thin films of pure n-alkanes on solid substrates. In this work, we were able to grow dotriacontane (n-C(32)H(66)) films without coexisting bulk particles, which allows us to isolate the contribution to the ellipsometric signal from a monolayer of molecules oriented with their long axis perpendicular to the SiO(2) surface. For these submonolayer films, we found a step in the ellipsometer signal at approximately 331 K, which we identify with a solid-solid phase transition. At higher coverages, we observed additional steps in the ellipsometric signal that we identify with a solid-solid phase transition in multilayer islands ( approximately 333 K) and with the transition to the rotator phase in bulk crystallites ( approximately 337 K), respectively. After considering three alternative explanations, we propose that the step upward in the ellipsometric signal observed at approximately 331 K on heating the submonolayer film is the signature of a transition from a perpendicular monolayer phase to a denser phase in which the alkane chains contain on average one to two gauche defects per molecule.