A heating or cooling roller comprises a stationary axle, at least one hydrostatic or hydrodynamic bearing element to support a rotary roller shell on the stationary axle, and a heatable or coolable heat transfer medium which flows through an annular gap between the stationary axle and the rotary roller shell; the roller shell has peripheral axially parallel orifices for the heat transfer medium which is supplied and discharged through at least one radial channel in the stationary axle and via at least one annular space between the roller shell and the stationary axle.