The invention relates to a method and a finishing train for hot-rolling starting material. Starting material is finished in several successive roll stands (110 n) in the finishing train, the material cooling off because of heat loss. The material has to be reheated in order for the temperature of the material not to drop below the predefined lower threshold temperature value at low speeds within and at the discharge end of the finishing train. In order to use as little energy as possible for said reheating process the reheating process within the finishing train is carried out for the first time only when the temperature of the material risks falling below the lower threshold temperature value for the first time relative to the direction of flow of the material because of heat loss. Furthermore, the temperature of the material during the reheating process is increased only to the point where the temperature of the material will not drop below the lower threshold temperature value (TU) while the material is conveyed onto a next heating device that is mounted downstream in the direction of flow of the material and until the material is discharged from the mill train.