In the context of emission-free electricity generation, the authors developed a novel hydrogen-oxygen combustor, which is based on swirl-stabilized combustion technology and steam dilution. Following previous burner characterization, the current study investigates the heat transfer conditions in the combustion chamber wall. To this end, a carefully controlled co-flow of air is used to cool the combustion chamber in an annular duct, which surrounds it. Temperature measurements enable the evaluation of the heat flux from the combustor flow to the walls, local wall temperatures, and the Nusselt numbers on the hot and the cold side. The extremely high wall temperatures, caused by the H2/O2 flame, can be reduced by steam dilution down to approximately 900 K. Even better cooling could be reached by using the dilution steam as the coolant before it flows to the plenum. The Nusselt numbers at the inner combustion chamber wall are in the order of 10 − 50 and increase with the thermal power and the steam dilution ratio.