The generation of wheel–rail-sliding frictional heat is often accompanied by transverse displacement of a wheel. To study the thermal problem of wheel–rail sliding friction at two-point contact, this paper uses an LM tread wheel and a 60 kg·m−1 rail as examples. A thermal–mechanical-coupled finite-element model of equal proportion wheel–rail sliding is established. A direct-coupling method is used to analyze the thermal–mechanical coupling of the wheel–rail interface under sliding contact. This model considers the temperature-dependent material properties and boundary conditions, such as thermal convection and thermal dissipation, in the process of nonstationary frictional-heat conduction. Firstly, the effects of different sliding speeds, axle loads, and contact modes on the temperature and stress fields of the contact area are analyzed. Then, the lubrication and cooling effects of friction modifiers on the rail top and rail gauge angle are compared. The results show that, at a sliding speed of 2 m/s and an axle load of 30 t under a sliding condition of 200 mm, on the top and side of the rail, the temperatures at the contact patch centers are 813 °C and 547.7 °C, respectively. Under different operating conditions, the rail-side temperature is 55–75% of that of the temperature at the rail top, and the rail-side contact and friction stress values are 76–96% of those at the rail top. This indicates that frictional thermal damage on the rail side cannot be ignored. With a lower sliding speed, the thermal response of the two contact patches is closer. The impact of axle load on the frictional temperature and stress on the rail side is more critical than the sliding speed. The optimal lubrication choice is overall lubrication, which can decrease the rail top temperature by 47.2% and frictional stress by 56.2%, as well as decreasing the rail side temperature by 70.3% and frictional stress by 77.4%.