A solution of the Reynolds equation for finite bearings with exponential film shape and variable viscosity is presented. The field of temperatures is also investigated, by solving the Energy equation. Therefore, the uncoupling of Reynolds and Energy equations is obtained, by using a relationship between viscosity and film thickness. The solution may be used either for plane or convergent curved surfaces with a satisfactory accuracy, as shown by the diagrams of pressure and temperatures. The formulas are given in closed forms, either for adiabatic films or constant temperature boundaries, thus allowing rapid calculations. Furthermore, formulas for the overall characteristics are available, which may be directly used in bearing design.