Abstract: Apparatus for cooling the end portions of a calender roll which has an elastic layer adjacent its peripheral surface and wherein the central portion of the peripheral surface is overlapped by a running web of paper or other material when the calender is in use. The width of the non-overlapped portions of the peripheral surface of the roll varies when a web having a first width is followed by a web having a different second width. This could lead to damage to the roll at the non-overlapped portions of the peripheral surface as a result of overheating by an adjacent rotary component of the calender. The end portions of the roll are cooled by discrete adjustable cooling devices which are movable along the respective non-overlapped portions of the peripheral surface in parallelism with the axis of the roll and each of which shares movements with a monitoring device which is to be maintained in a selected position relative to the adjacent marginal portion of a running web.