This study aims to predict the feasibility and the performances of an innovative recovery system. It couples a double acting Stirling engine to the exhaust hot gas of internal combustion engines drive shaft. The behaviour of a micro-cogeneration system using Stirling engine is investigated. Referring to previous energetic analyses, exergetic model is set up in order to quantify the exergy destruction and efficiencies in each part of the recovery exhaust system. The repartition of the exergy fluxes in each part are determined and represented in Grassmann diagram. Possible solutions to improve the overall exergy efficiency of the micro-cogeneration unit were proposed. The performance of the Stirling engine was evaluated under different operating conditions. Effects of certain parameters including charge pressure, rotational speed, hot exhaust gas temperature and cooling water temperature are systematically studied. The effect of hot-side and cold-side exchange surfaces on the power and efficiency of the Stirling engine as well as on the efficiency of the global micro-cogeneration unit is investigated. The performance of the Stirling engine using three different working fluids: nitrogen N2, helium He and hydrogen H2 is estimated. Results can be useful for scientists and engineers to design an appropriate and efficient micro-cogeneration unit.