The present invention relates to a method of maintainance of a furnace (21) for the catalytic reforming of a hydrocarbon reaction mixture, comprising catalyst tubes (26) in which the maximum temperature of each tube is determined and monitored on the basis of a series of continuous tube temperature measurements and of a second series of discrete temperature measurements, the change in maximum temperature measured during any use of the furnace is continuously monitored, using a SCADA-type data acquisition system, these temperature measurements are converted into a remaining lifetime for each tube, and the replacement of the tubes at the end of life is planned according to the programmed furnace maintainance stoppages.