A method produces a product gas rich in hydrogen. A starting material including carbon is split via pyrolysis, and the resulting gas is mixed with water vapor to increase the hydrogen content and heated. The heat necessary comes from the combustion of the produced pyrolysis coke. The heat necessary for individual process steps is fed via a heat transfer medium circuit having a heating zone heated via flue gas from the pyrolysis coke firing. The gas/water vapor mixture is subsequently heated in a reaction zone. The heat transfer medium heats the starting material in a pyrolysis zone indirectly, without directly contacting the starting material, is cooled in a cooling zone, and subsequently returns to the beginning of the circuit. Upstream of the heating zone, the heat transfer medium is preheated via the hot product gas.