The method comprises a first stage of transforming carbon precursor material into carbon by heating, with the resulting gaseous effluent being extracted continuously, and a second stage of high temperature heat treatment under low pressure with the resulting gaseous effluent being extracted continuously. The first and second stages are performed one after the other in the same oven by proceeding, after the end of the first stage, with the steps of switching the gaseous effluent outlet from the oven to interrupt a connection with a first extractor device and to establish a connection with a second extractor device, of adjusting the pressure inside the oven to the value required for the second stage, and of adjusting the heating temperature of the oven starting from the temperature reached at the end of the first stage. It is also possible to switch temperature measurement from at least one first sensor to at least one second sensor different from the first. During the second stage, any alkali metal such as sodium contained in sublimed form in the gaseous effluent coming from the oven can be neutralized, e.g. by injecting CO.sub.2 into an effluent exhaust pipe.