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Emission regulations have become increasingly stringent in recent years. Current regulations need the development of a new worldwide driving cycle which gives greater weight to the pollutants emitted during transient phases or cold starts. Powertrains contain a large number of components such as multistage turbocharger systems; exhaust gas recirculation, after-treatment devices and sometimes an electric motor. In this context, 0D predictive models of heat transfer in the exhaust line, calibrated with experimental data, are particularly interesting. Many investigations are related to the development of precise control laws in order to optimize the light-off of after-treatment elements during the engine starting phase. A better understanding of the thermal phenomena occurring in the exhaust line is necessary. To study the heat transfer in the exhaust line of a Diesel engine during transient conditions, the temperature in the exhaust line must be known precisely.