In our previous papers, we attempted to predict traction coefficient by combining oil film rheological models and heat conduction models. The rheological characteristic was considered by dividing rheological region in viscous and plastic. In addition, we formed a very tiny thin film sensor on rolling surface, and challenged to measure temperature change directly when the sensor passed through inside contact portion. But physical interpretation of shear flow transition between two rheological regions was still unclear. Since the plastic model was determined as empirical formula, its universality was also insufficient. In this paper, we define boundary continuity of shear flow transition between the two rheological regions in a new interpretation. Further utilizing this result, we propose a theoretical approach to determine the plastic model by using rheological parameters in viscous region. When the model is derived theoretically and if it could express physical phenomena as a function of actual temperature, we need accurate oil film temperature estimation. In that case, we show that it is effective to make the temperature prediction model in vicinity of contact portion. This is because the time constant of contact film thermal diffusion is small, it makes sense as an effective prediction of traction coefficient. Also by the thin film sensor measurement, the time constant is actually confirmed to be extremely small.