We study the melting of an ultrathin lubricant film under friction between atomically flat surfaces at temperature dependencies of viscosity described by Vogel-Fulcher relationship and by power expression, which are observed experimentally. It is shown that the critical temperature exists in both cases the exceeding of which leads to the melting of lubricant and, as a result, the sliding mode of friction sets in. The values of characteristic parameters of lubricant are defined, which are needed for friction reduction. In the systems, where the Vogel-Fulcher dependence is fulfilled, it is possible to choose the parameters at which the melting of lubricant takes place even at zero temperature of friction surfaces. The deformational defect of the shear modulus is taken into account in describing the lubricant melting according to the mechanism of the first-order transition.