A steam generator is provided. The steam generator has a combustion chamber having a peripheral wall formed at least partially from gas-proof, welded steam generator pipes, at least two additional inner walls formed at least partially from additional steam generator pipes which are arranged inside the combustion chamber. The inner walls are connected one behind the other on the flow medium side by an intermediate collector. The steam generator has a high service life and is reliable. The flow medium on the inlet of the inner wall upstream of the intermediate collector has a lower temperature than that of the flow medium on an inlet of the peripheral wall.