The high temperature and heat flux in a rocket combustion chamber make an active cooling indispensable. In this work tests will be presented that were performed with a cylindrical research combustion chamber segment that is divided into four sectors around the circumference each containing cooling channels with a different aspect ratio. For methane as cooling fluid, due to the vicinity to the critical point, it may come to a separation of a hot gas-like layer at the wall and the cold liquid-like bulk flow. This effect is known as heat transfer deterioration (HTD) and leads to a locally disturbed heat transfer coefficient and a rising hot gas sidewall temperature. The main parameter for this effect are also analysed experimentally. Based on the experiments, numerical simulations were performed. The comparison between simulated and measured values shows satisfactory small deviations. In the vicinity to the critical point, especially when it comes to HTD, the simulations show a systematic deviation and over-predict the hot gas sidewall temperature