A roll, specifically a paper machine press roll, with a hollow rotatable roll body features a roll shell and on at least one of its two ends a hollow roll journal. A guide body which is stationary or fastened to the roll body extends through the interior of the roll body and forms with the roll shell a channel system through which a tempering medium flows. For purposes of using air as tempering medium, a pressure blower and/or a suction blower are connected to the channel system. The channel system and the blower(s) are so dimensioned that an air flow velocity above 10 m/sec will materialize in the channel system.