Abstract: For conducting exothermic catalytic reactions, e.g., production of methane from CO.sub.x and H.sub.2, a reactor is cooled internally by indirect heat exchange with a single heat exchanger provided in the reactor feed inlet region with a gradually increasing surface intensity (defined as the product of the overall coefficient of thermal conductivity, (h), of the tube wall times the cooling surface density, m.sup.2 /m.sup.3) reaching a maximum intensity at a central zone of the heat exchanger where the preponderant cooling occurs. A zone of gradually decreasing cooling surface intensity may also be provided at the outlet end of the reactor, and uncooled adiabatic zones may be incorporated in the zones immediate the inlet and outlet ends of the reactor.