Cylindrical carbon blanks are assembled into one or more upright stacks which are advanced stepwise in an upward direction in one or more upright tubes which insulate the column or columns from the surrounding atmosphere. The blanks in the upright tube or tubes are preheated by exchanging heat with an inert gas, such as pure argon, and the preheated blanks are thereupon conveyed along one or more horizontal path sections into the upper end of an additional tube wherein the blanks are heated to graphitizing temperature by a series of electrode pairs. The thus obtained graphite electrodes are cooled by inert gas which is thereupon admitted into the upright tube or tubes to preheat fresh carbon blanks.