Method and plant for pre-heating, transforming and melting a metal charge comprising metal scrap, in an electric arc furnace associated with a tunnel to transport, pre-heat and discharge the scrap. The furnace comprises a hearth and a roof through which the electrodes pass. The method provides that the furnace is weighed at least periodically in order to detect the quantity of discharged scrap present inside the furnace itself, that the temperature of the liquid bath inside the furnace is detected at least periodically and that at least the discharge delivery of the scrap inside the furnace is detected by weighing and is regulated in order to maintain the temperature of the liquid bath around a pre-determined value.