A device for cooling a material web in a web-fed rotary printing machine, includes a heating device for producing waste heat for evaporative cooling of a cooling medium, and a cooling configuration through which the cooling medium is directable for web cooling. A first quantity of the cooling medium is evaporated and a second quantity is cooled by removal of heat of evaporation. A vapor generator produces vapor at least partly by the waste heat from the heating device. At least one vapor-jet vacuum nozzle is operatable by the vapor for producing a negative pressure. The cooling medium is to be subjected to negative pressure in a negative-pressure chamber for at least partial evaporation and for cooling. A dryer including the cooling device, a printing machine including the cooling device or the dryer and a cooling method are also provided.