A catalyst, e.g., a cracking catalyst, and a part of the regeneration fumes are drawn off from the dense catalytic bed of a second regenerator (9) and are introduced by force of gravity into an external exchanger (21) at a junction point beneath the level of the dense bed of the second regenerator. The heat exchange takes place in the bottom part of the exchanger below the junction point. Between the bottom end of the exchanger and the region above the junction point a dense bed zone is formed at a level which is substantially at the height of the dense bed in the regenerator and a discharge zone (27), of suitable size, for the regeneration gases and fluidization gas. The gases and fumes from the exchanger are removed in the diluted fluidized phase from the second regenerator through a conduit (28), while the catalyst is recycled in to the bed of the first regenerator through a conduit (34).