  Melting of an ultrathin lubricant film confined between two atomically flat
surfaces is we studied using the rheological model for viscoelastic matter
approximation. Phase diagram with domains, corresponding to sliding, dry, and
two types of $stick-slip$ friction regimes has been built taking into account
additive noises of stress, strain, and temperature of the lubricant. The stress
time series have been obtained for all regimes of friction using the
Stratonovich interpretation. It has been shown that self-similar regime of
lubricant melting is observed when intensity of temperature noise is much
larger than intensities of strain and stress noises. This regime is defined by
homogenous distribution, at which characteristic stress scale is absent. We
study stress time series obtained for all friction regimes using multifractal
detrended fluctuation analysis. It has been shown that multifractality of these
series is caused by different correlations that are present in the system and
also by a power-law distribution. Since the power-law distribution is related
to small stresses, this case corresponds to self-similar solid-like lubricant.
