The distribution of “effective viscosity”—assumed dependent on local shear and temperature—is obtained via iteration between the “long bearing” momentum and energy equations. In this treatment the shaft is isothermal and the bearing conducts heat only in the radial direction. This last assumption leads to essential simplifications: the bearing is replaced by an equivalent homogeneous boundary condition of the energy equation, which thus becomes amenable to solution by the Galerkin-Kantorovich method. The resulting effective viscosity is used to calculate the performance of finite journal bearings.