The present invention concerns an isothermal reactor (1) for carrying out exothermal or endothermal heterogeneous reactions comprising: - a substantially cylindrical outer shell (2) with longitudinal axis (X), - at least one catalytic bed (6) extending in the shell (2) and comprising opposite perforated side walls (7, 8) respectively for the inlet of a gaseous flow of reactants and for the outletof a gaseous flow comprising reaction products, and - a heat exchange unit (12) immersed in said at least one catalytic bed (6) and crossed by a heat exchange fluid, characterised in that said heat exchange unit (12) comprises at least one succession of heat exchangers (13) arranged substantially parallel to each other and substantially parallel to the direction in which said at least one catalytic bed (6) is crossed by said gaseous flow of reactants.