In the study, based on the micropolar fluid flow equation for a “thin layer”, the continuity equation, the equation describing the profile of the molten contour of the guide coated with a low-melting metal alloy, and the equation for the mechanical energy dissipation rate, asymptotic and exact self-similar solution has been found for the zero (without considering the melting) and first (considering the melting) approximation of wedge-shaped support with the slider support profile adapted to the friction conditions and the low-melting metal coating of the guide surface. The research has taken into account the pressure dependence of the lubricant rheological properties and the melt having micropolar properties in the laminar flow regime. Analytical dependencies have been obtained for the molten surface profile of the low-melting metal coating of the guide and the field of velocities and pressure for the zero and first approximations. Also, the basic performance characteristics of the friction pair under consideration have been determined: the bearing capacity and the friction force. The impact of parameters determined by the coating melt, adapted to the support profile friction conditions, and the parameter characterizing the pressure dependence of the lubricant viscosity on the bearing capacity and friction force has been estimated.