An air heater for small spaces, in particular movable spaces, such as caravans, motorhomes, boats or the like, has a heat exchanger (2) inserted between a cylindrical combustion chamber (5), fired in particular by gas, and an outer envelope (3) that surrounds the combustion chamber with a certain gap, forming a heating space (6) between a heating tube (1) and an inner envelope (4) of the inserted heat exchanger and an annular space (7) for an air flow to be heated between the inner envelope and the outer envelope (3). The inserted heat exchanger (2) is an extruded section formed of an inner envelope (4) with radially projecting inner ribs (8) and outer ribs (10). The inner and outer ribs are similarly arranged on opposite sides of the inner envelope. The outer edges (12) of the outer ribs (10) are provided with a crossridge (13) that projects at least on one side and whose outer surface faces the outer envelope (3) with a certain gap .