A reaction chamber (E) comprises a calender reactor (5) comprising a device (4) for introducing a feedstock; a device (6) for carrying off the treated feedstock; at least two elementary reaction cells (52), not contiguous to one another, each one consisting of an individual feedstock distributor, an individual collector of the treated feedstock, and a catalytic bed, the cells being separated from one another by a channel (51); at least one device (V) for circulating a heat-carrying fluid in each channel (51); at least n partitions (S) for separating the flow of the heat-carrying fluid, n being an integer greater than or equal to 1; and at least n+1 means (T) for heating the heat-carrying fluid. The chamber can be used for performing the catalytic reforming of naphtha under low pressure.