A high-temperature operating fuel-cell module comprising: a fuel-cell stack that generates power by utilizing an electrochemical reaction of oxidant gas supplied to a cathode and reformed gas supplied to an anode; a fuel-cell stack container in which the fuel-cell stack is contained, cathode off-gas discharged from the cathode of the fuel-cell stack flowing in a space of the fuel-cell stack container in which the fuel-cell stack is contained; a cathode off-gas collector that is provided in the fuel-cell stack container, the cathode off-gas collector being a space in which the cathode off-gas is collected; an anode off-gas passage through which anode off-gas discharged from the anode of the fuel-cell stack flows; and a combustor that combusts the cathode off-gas collected in the cathode off-gas collector and the anode off-gas flowing through the anode off-gas passage, the combustor comprising: a combustion chamber that is a space in which the anode off-gas and the cathode off-gas are mixed and combusted, an ejector that is connected to the anode off-gas passage and ejects the anode off-gas into the combustion chamber, and a diffusion plate that surrounds the ejector so that the ejector is located at the center of the diffusion plate, and ejects the cathode off-gas collected in the cathode off-gas collector into the combustion chamber, wherein the fuel-cell stack container includes an air heat exchanger that exchanges heat between the oxidant gas that has not been supplied to the cathode of the fuel-cell stack yet and the cathode off-gas flowing in the fuel-cell stack container, characterized in that a side wall of the fuel-cell stack container includes an inner wall and an outer wall; and the air heat exchanger is constituted by the inner wall, the outer wall, and a flow passage that is a space between the inner wall and the outer wall and through which the oxidant gas flows, the air heat exchanger exchanging heat between the oxidant gas and the cathode off-gas with the inner wall interposed therebetween. a fuel-cell stack that generates power by utilizing an electrochemical reaction of oxidant gas supplied to a cathode and reformed gas supplied to an anode; a fuel-cell stack container in which the fuel-cell stack is contained, cathode off-gas discharged from the cathode of the fuel-cell stack flowing in a space of the fuel-cell stack container in which the fuel-cell stack is contained; a cathode off-gas collector that is provided in the fuel-cell stack container, the cathode off-gas collector being a space in which the cathode off-gas is collected; an anode off-gas passage through which anode off-gas discharged from the anode of the fuel-cell stack flows; and a combustor that combusts the cathode off-gas collected in the cathode off-gas collector and the anode off-gas flowing through the anode off-gas passage, the combustor comprising: a combustion chamber that is a space in which the anode off-gas and the cathode off-gas are mixed and combusted, an ejector that is connected to the anode off-gas passage and ejects the anode off-gas into the combustion chamber, and a diffusion plate that surrounds the ejector so that the ejector is located at the center of the diffusion plate, and ejects the cathode off-gas collected in the cathode off-gas collector into the combustion chamber, wherein the fuel-cell stack container includes an air heat exchanger that exchanges heat between the oxidant gas that has not been supplied to the cathode of the fuel-cell stack yet and the cathode off-gas flowing in the fuel-cell stack container, characterized in that a side wall of the fuel-cell stack container includes an inner wall and an outer wall; and the air heat exchanger is constituted by the inner wall, the outer wall, and a flow passage that is a space between the inner wall and the outer wall and through which the oxidant gas flows, the air heat exchanger exchanging heat between the oxidant gas and the cathode off-gas with the inner wall interposed therebetween. a combustion chamber that is a space in which the anode off-gas and the cathode off-gas are mixed and combusted, an ejector that is connected to the anode off-gas passage and ejects the anode off-gas into the combustion chamber, and a diffusion plate that surrounds the ejector so that the ejector is located at the center of the diffusion plate, and ejects the cathode off-gas collected in the cathode off-gas collector into the combustion chamber, wherein the fuel-cell stack container includes an air heat exchanger that exchanges heat between the oxidant gas that has not been supplied to the cathode of the fuel-cell stack yet and the cathode off-gas flowing in the fuel-cell stack container, characterized in that a side wall of the fuel-cell stack container includes an inner wall and an outer wall; and the air heat exchanger is constituted by the inner wall, the outer wall, and a flow passage that is a space between the inner wall and the outer wall and through which the oxidant gas flows, the air heat exchanger exchanging heat between the oxidant gas and the cathode off-gas with the inner wall interposed therebetween.