Abstract: n this paper, a numerical solution of; the thermal-elastohydrodynamic lubrication of, rolling-and sliding cylinder is extended by considering more rigorous analysis of the energy, equation, including the effects of the second coefficient of viscosity and the heat arising from compression of the lubricant. Both the Barus and Roelands equations to describe the pressure-temperature dependency of viscosity have been used during the calculation. Mea .surements of the coefficient of friction have also been carried out on the two-disc machine. At the same time, the effects of applying the time-dependent viscosity model and the By ring fluid model have been studied. The theoretical results predicted by this model show that the second coefficient of viscosity and the heat from compression of the lubricant only have such a small influence on the coefficient of friction that their effects can be neglected. The applying of Roelands, equation can make the predicted coefficient of friction much smaller than by applying Barus equation and fit the experimental results much better. However, the discrepancy between the theory and experiments is still quite large. The results also show that both Newtonian fluid model and the time-dependent model couldn't explain the tractive behaviour well. The only model which can predict the tractive behaviour is Eyring model, the descrepancy of which comparedwith experimental results. Is only about 10%.