The invention relates to a method for operating a paper machine (10) for producing paper, paperboard or cardboard, comprising a conveyor device (16) by means of which at least one fibrous material web (14) produced from a fibre suspension is conveyed in a conveyor direction, at least one drying region (20) in which the fibrous material web (14) which is conveyed through said drying region (20) is dried using at least one drying cylinder (26) to which a first medium for drying the fibrous material web (14) is supplied, and at least one smoothing cylinder (28) which connects to said drying cylinder (26) in the conveyor direction and by means of which said fibrous material web (14) is smoothed on at least one side, wherein a second medium is fed to the smoothing cylinder (28) for the purpose of heating said smoothing cylinder (28), and the first medium is conducted away from the drying cylinder (26) and is supplied, as a source of heat, to a heat pump (34) by means of which the second medium is heated.