A catalyst regeneration process effected in an apparatus which comprises two regeneration chambers, a heat exchanger, means for withdrawing from the second chamber a controlled fraction of hot catalyst for the purpose of maintaining the temperature in that chamber substantially at a first desirable value of less than 950.degree. C., and preferably at 910.degree. C., means for transferring this fraction of hot catalyst to the heat exchanger for the purpose of cooling it, means for the discharge of the cooled catalyst from the heat exchanger and the reinjection of the cooled catalyst into the first chamber, and means, controlled by the means for measuring the temperature in the first chamber, for regulating the supply of combustion fluid to the first chamber for the purpose of maintaining said temperature substantially at a second desired value lower than 730.degree. C. and preferably ranging from 650.degree. to 710.degree. C.