This work presents a numerical study of hydrodynamic lubrication of a plain journal bearing with taking into account the thermal effects including couple stress effects due to lubricant additives. The viscosity variation with film-temperature was taken into account. The studied domain is represented by the lubricating film, the bush and the rotary shaft. The analysis includes the solution of the different thermohydrodynamic equations such as: modified Reynolds equation, three-dimensional energy equation and velocity distribution equations in the lubricating film domain, as well as the heat transfer equation in both the bush and the shaft with convenient conditions at the two interfaces. Also, the cavitation has been considered according to Reynolds boundary condition. A computer program has been developed to solve simultaneously the aforementioned equations using finite difference method. The obtained results of the developed code have been compared to that of the literature, a good agreement was shown. It has been shown that including lubricant with additives acts like a non-newtonian fluid. It has been found that the couple stress effect enhances the maximum oil pressure as well as the load capacity and reduces the friction coefficient.