The invention relates to a device and a method for cooling a roll. The roll concerned can be a roller in a roll stand or a measuring roll. The device comprises a cooling shell having a cross section in the shape of a section of a circular arc, for covering a surface region of the roll (200), wherein, in the region of an edge of the cooling shell, a bearing is formed with a pivot joint (120) with an axis of rotation running perpendicular to the circular arc-shaped cross-section, for pivoting the cooling shell about the axis of rotation. According to the invention, in order to ensure that the size of the cooling gap during the rolling operation or during the operation of a measuring roll is always autonomously optimally set, the bearing has a degree of freedom in radial direction r with respect to the circular arc-shaped cross-section of the cooling shell, such that the cooling shell is mounted in the bearing in such a way as to be freely movable in the radial direction.