The fuel cell battery (1) has an integrated heat exchanger (4) which is arranged between a heat insulating jacket (12) and a stack (10) of high temperature fuel cells (2). There is a chamber (3), preferably at least two chambers for afterburning, between a periphery (14) of the cell stack and the heat exchanger. The heat exchanger is provided for a heat transfer from an exhaust gas (7) to a gaseous oxygen carrier (5). There are arranged on the stack periphery (14), outside or inside the chamber or chambers respectively, inlet points (25a) for the oxygen carrier, on the one hand, and outlet points (25b, 26b) for non-converted educts, namely a fuel gas (6) and the oxygen carrier, on the other hand. The heat exchanger (4) includes a passage system (4) through which the exhaust gas (7) and the oxygen carrier (5) flow largely in transverse planes disposed perpendicular to the axis of the cell stack (10) in one operating state of the battery. The exhaust gas can be led off through axially directed collecting passages (47") which are arranged in a peripheral region of the heat exchange. Parts of the heat exchanger, which are disposed between the peripheral region and the cell stack, form a shield for screening the cell stack from the collecting passages with respect to a thermal influence.