The invention relates to a press tower (01) of a printing press having a plurality of printing units (08) which are arranged above one another and print on the same side of a web (02; 02'), for multiple-colour printing on both sides of a web (02; 02) which is guided through the press tower (01) and is formed from uncoated or slightly coated newspaper, wherein the printing units (08) in each case have a printing-unit cylinder (11; 13) which is configured as a transfer cylinder (11; 13) and a printing-unit cylinder (12; 14) which is configured as a forme cylinder (12; 14), and an inking unit (09) which interacts with said forme cylinder (12; 14) and is configured as a roller inking unit (09) with at least one axially oscillating roller (19; 21) and an ink metering system (18) which can be set zonally with regard to the printing ink to be introduced, wherein the printing units (08) are configured or are at least operated as dry offset printing units (08), by the forme cylinder (12; 14) carrying at least one printing forme which is configured for waterless offset printing, and by the printing unit (08) being configured without a dampening unit, or at least without an operating dampening unit, and wherein at least the forme cylinders (12; 14) and one or more rollers (19; 21) of the inking unit (09) of each printing unit (08) are configured such that their temperature can be controlled, wherein the forme cylinders (12; 14) of at least two or all of the printing units (08) of the press tower (01) which interact with the same one side of the web (02) are in thermal interaction with temperature-control circuits (37), the temperatures of which can be controlled independently of one another.