To have knowledge about the gas and material temperatures in the exhaust system of today's vehicles is of great importance. These temperatures need to be known for component protection, control- and diagnostic purposes. Today mostly map-based models are used which are not accurate enough and difficult to tune since it consist of many parameters. In this thesis physically based models are developed for several components in the exhaust system. The models are derived through energy balances and are more intuitive compared to the current map-based models. The developed models are parameterized and validated with measurements from wind tunnel experiments and driving scenarios on an outdoor track. The engine out model is modeled theoretically and is therefore not parameterized or validated. The model for the temperature drop over the exhaust manifold could not be validated due to the pulsations occurring in the exhaust manifold, however suggestions on how to solve this problem are given in this report. The models for the turbocharger, the catalyst and the downpipe are parameterized and validated with good results in this thesis. The mean absolute error for the validation data set for the turbocharger is 0.46 % and 1.01 % for the catalyst. The mean absolute percentage error for the downpipe is 1.07 %.