The realization of movement by railway vehicles creates a problem that is connected to the wear process for elements of a tribological wheel–rail system. Wheel–rail wear is a complex phenomenon that depends on many factors. One of the main wear zones is the contact area between a wheel flange and a rail gauge. As is well known, wear in this contact zone occurs when a railway vehicle moves on curved parts of track, realizes tractive, braking efforts or moves in a high-speed mode. In this case, the solution of this kind of wear problem can be found by means of lubricant implementation. The choice of a lubricant requires information about contact characteristics at the moment of a vehicle’s movement. This paper focuses on the modeling of the temperature process in the contact between a wheel flange and a rail gauge. Examples of temperature calculation with some experimental data as input for this computation are presented. The obtained values of the temperature allow for making the correct choice of lubricant type.