A rheological model and a thermodynamic model are proposed for describing the melting of an ultrathin lubricant film between atomically flat solid surfaces. Hysteresis phenomena are considered, allowing for the stress and strain dependence of the lubricant shear modulus. The self-similar regime of lubricant melting is studied taking the additive noncorrelated noise of basic parameters into account. The regions of dry, sliding, and stick—slip friction are determined in the phase diagram. Shear stress time series are obtained by numerically analyzing the Langevin equation and are then subjected to multifractal fluctuation analysis. The dependence of the stationary friction force on the lubricant temperature and on the shear velocity of rubbing surfaces is investigated.