A hydrostatically supported roll has several hydrostatic support elements supporting the inner circumference of a rotating hollow roll. The hydrostatic elements are supported on the stationary crosshead that extends through the rotating roll to form a clearance space therewith. Each hydrostatic element has support pockets supplied with a first pressurized fluid via choke canals and branch lines connected to a flow-controlled pump delivering a constant volume of first pressurized liquid, regardless of the counterpressure in the support pockets. The first pressurized liquid fed to the support pockets is temperature-controlled. The support pockets are separated from essentially closed pressure chambers, which are supplied with a second pressure-controlled pressurized liquid from separate feedlines for pressing the hydrostatic elements against the inner circumference of the hollow roll to support same. The second pressurized liquid is not communicated to the inner circumference of the hollow roll. Therefore, independent of any pressure change in the pressure chambers, the same quantity of first pressurized liquid passes over the edges of the support pockets to ensure that the amount of heat transferred to the inner circumference of the hollow roll remains constant.