In order to investigate the heat load of the combustion chamber fed with gaseous oxygen and gaseous methane, a rocket combustion chamber with a single coaxial shear injector is tested. The hot firing tests are conducted with gaseous methane and gaseous oxygen at a mass ratio of oxidizer to fuel of 2.647 and at a pressure of 2MPa. Wall temperatures are measured along the axis of the chamber and the wall heat fluxes are calculated based on inverse heat conduction approach. To better analyze the experimental results, numerical simulations are performed applying the commercial CFD code ANSYS Fluent. The eddy dissipation concept model is adopted to model turbulent combustion. Mesh independency studies have been performed prior to any further analyses. The ultimate target is to compare the heat fluxes obtained from simulation with the experimental data. The comparison demonstrates that the simulation approach adopted is capable to predict wall heat fluxes in a rocket combustor with sufficient accuracy and the relative deviation is 17% at maximum heat flux. Hot gas temperature distribution and flow field structures are also investigated for a better understanding of the experimentally determined heat flux profile.