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Fuel consumption after a cold start remains one of the major goal of carmakers. The high friction losses due to a low oil temperature are the main sources of the consumption excess during the warm-up. To improve the prediction of these losses, the local oil temperature in friction areas must be well represented. The local equilibrium temperature depends both on the heat flux generated by friction and on the oil flow rate. The aim of this work is to represent the thermo-hydraulic behavior of oil loops during the warm-up of a cold start. Oil pump efficiency is evaluated considering Poiseuille and Couette flow contributions on the leaks of the pump. Computed results are validated on results gained on a test bed. The hydraulic behavior of bearings is modeled from a theoretical approach. The effects of bearing deformation are rendered by a global elasticity coefficient calibrated from results in a previous paper.