Bars and wire rods are rolled from billets or blooms in the disclosed process which includes a primary rolling step resulting in an intermediate material, a secondary rolling step and a heat treatment. The primary (first) rolling step includes rolling the billet or bloom steel material into an intermediate material at a mass flow rate to enable it to be maintained during the primary rolling within a temperature range corresponding to a predetermined deformation resistance level of the steel material. This predetermined deformation resistance level is selected so as to take advantage of an opportunity to save energy. The intermediate material resulting from primary rolling is coiled and its temperature is adjusted so as to maintain the intermediate material at a desired starting temperature for the secondary rolling step. The desired starting temperature for secondary rolling is related to a desired starting temperature for the heat treatment following the secondary rolling enabling heat treatment to be carried out in line.