The development of efficient low emission combustion systems requires methods for an accurate and reliable prediction of combustion processes. Computational Fluid Dynamics (CFD) in combination with combustion modelling is an important tool to achieve this goal. For an accurate computation adequate boundary conditions are crucial. Especially data for the temperature distribution on the walls of the combustion chamber are usually not available. The present work focuses on numerical simulations of a high momentum jet flame in a single nozzle FLOX® type model combustion chamber at elevated pressure. Alongside the balance equations for the fluid the energy equation for the solid combustor walls is solved. To assess the accuracy of this approach, the temperature distribution on the inner combustion chamber wall resulting from this Conjugate Heat Transfer (CHT) simulation is compared to measured wall temperatures. The simulation results within the combustion chamber are compared to detailed experimental data. This includes a comparison of the flow velocities, temperatures as well as species concentrations. To further assess the benefit of including the solid domain in a CFD simulation the results of the CHT simulation are compare d to results of a CFD computation where constant temperatures are assumed for all walls of the combustion chamber.