The single element GCH 4 /GOx rocket combustion chamber developed at the Technische Universität München has been computed using Large Eddy Simulation. The aim of this work is to analyze the flow and combustion features at high pressure, with a particular focus on the prediction of wall heat flux, a key point for the development of reusable engines. The impact of the flow and flame, as well as of the model used, on thermal loads is investigated. Longitudinal distribution of wall heat flux, as well as chamber pressure, have been plotted against experimental data, showing a good agreement. The link between the heat released by the flame, the heat losses and the chamber pressure has been explained by performing an energetic balance of the combustion chamber. A thermally chained numerical simulation of the combustor structure has been used to validate the hypothesis used in the LES.