Abstract: A roll of controllable flexure having a cylindrical inner part and a tubular outer part surrounding the inner part and mounted rotatably at both its ends on the inner part. A heating strip is disposed along a generatrix on the inner part. At least one electrical temperature sensor is disposed in the inner part in the immediate vicinity of the heating strip and at least one additional electrical temperature sensor is disposed on the opposite side of the inner part. The two temperature sensors are connected to a temperature difference measuring apparatus and control an electrical regulating circuit to which a power circuit containing the heating strip is connected. The power delivered to the heating strip is so regulated that a preset temperature difference between the heated and unheated sides of the inner part is maintained. The different thermal elongation of the unheated and heated sides of the inner part produces an arching of the inner part which is transmitted to the outer part.