The climate emergency due to the growing concentration of Greenhouse Gases (CO₂ above all) in the atmosphere and the tightening legislative regulations in terms of emissions represent the triggering point of the hybridization and electrification trends in recent years, aimed at moving more and more towards sustainable mobility solutions. The goal of this thesis work is to develop a lumped parameters model aimed at predicting the thermodynamic behaviour of the lubricating oil and the clutches of a P2 on-axis module for Mild Hybrid, Full Hybrid and Plug-in Hybrid vehicles. At first, an introduction to the legislative background and to the main hybrid architectures has been discussed.