A high-temperature electrolysis reactor, comprising an alternating stack of two groups of distinct stages, including: - a group of a plurality of stages referred to as electrochemical stages, each consisting of an individual electrolysis cell (C1, C2, C3) of the SOEC solid oxide type, formed from a cathode (2.1, 2.2,...), from an anode (4.1, 4.2,...) and from an electrolyte (3.1, 3.2...) inserted between the cathode and the anode, and of two interconnectors (5.1, 5.2), each suitable for electrical and fluid interconnection, arranged either side of the individual cell (C1, C2), - a group of at least one stage referred to as thermal regulation stage(s), consisting of at least one electrical contact element allowing the gases to pass and of two interconnectors (5.2, 5.3) each suitable for electrical and fluid interconnection, arranged either side of the contact element, the contact element being a metal grid, a set of discrete metal wires or a porous electron-conducting substrate, the interconnectors of the electrochemical stages and of the thermal stage(s) being suitable for both: • circulating, through the stack, steam (EH 2) or a mixture of steam H 2 O and of carbon dioxide CO 2, a draining gas, such as air, (E(O 2)), and a heat-exchange gas (EH 2), • recovering the hydrogen H 2 produced (SH 2) or the synthesis gas (mixture of carbon monoxide CO and of hydrogen H 2) produced at the cathodes of the cells, the oxygen O 2 produced (S(O 2)) at the anodes of the cells and the draining gas, and the heat-exchange gas (SH 2) at the outlet of the elements, those of the interconnectors intended for the electrochemical stages being also suitable for distributing both steam (EH 2) or the mixture of steam H 2 O and of carbon dioxide CO 2 to the cathodes of the cells, and the draining gas (E(O 2)) to the anodes of the cells, while those of the interconnectors intended for the thermal regulation stage(s) are suitable for distributing solely the heat-exchange gas to the electrical contact element(s) allowing the gases to pass. - a group of a plurality of stages referred to as electrochemical stages, each consisting of an individual electrolysis cell (C1, C2, C3) of the SOEC solid oxide type, formed from a cathode (2.1, 2.2,...), from an anode (4.1, 4.2,...) and from an electrolyte (3.1, 3.2...) inserted between the cathode and the anode, and of two interconnectors (5.1, 5.2), each suitable for electrical and fluid interconnection, arranged either side of the individual cell (C1, C2), - a group of at least one stage referred to as thermal regulation stage(s), consisting of at least one electrical contact element allowing the gases to pass and of two interconnectors (5.2, 5.3) each suitable for electrical and fluid interconnection, arranged either side of the contact element, the contact element being a metal grid, a set of discrete metal wires or a porous electron-conducting substrate, • circulating, through the stack, steam (EH 2) or a mixture of steam H 2 O and of carbon dioxide CO 2, a draining gas, such as air, (E(O 2)), and a heat-exchange gas (EH 2), • recovering the hydrogen H 2 produced (SH 2) or the synthesis gas (mixture of carbon monoxide CO and of hydrogen H 2) produced at the cathodes of the cells, the oxygen O 2 produced (S(O 2)) at the anodes of the cells and the draining gas, and the heat-exchange gas (SH 2) at the outlet of the elements,