To product multi-grade oil like engine oil, a sort of mineral base oil is mixed with a fundamental additive liquid package and a polymer liquid as viscosity index improver in order to improve the lubricating property of oil. That is, engine oil is the mixture of more than two fluids. In this paper, it will be systematically organized the governing equation describing non-Newtonian thermo-hydrodynamic lubrication related with the mixture of incompressible fluids based on the principle of continuum mechanics. Then, in order to find how the thermal analysis effect on the bearing performance lubricated with the mixture of multi-fluids, it will be compared to the performances between the mixture of each liquid to be blended and multi-grade engine oil as a single fluid in a high speed journal bearing. It is found that, in the case of lower viscosity oil, the difference of pressure distribution between the above two cases turns out to be existed, even if the load capacity is same level.