Abstract: The heating and cooling arrangement (3, 4) for an extrusion cylinder comprises a copper strip (4) bent aside at right angles at its ends (6, 7) and twisted by 45.degree., the middle portion (8) of which rests upon the extrusion cylinder (1) as well as a band-shaped flexible heating element (3) disposed over the middle portion (8). The cooling elements (4) are disposed on a cylinder section (b 5) at regular intervals over the whole periphery thereof. Two copper wires led through the end regions (9, 10) of the middle portions (8) of the cooling elements (4) fasten the same to the surface of the extrusion cylinder (1). The heating element has two outer metal sheets (15, 16), an insulating layer (17) lying therebetween, as well as heating wires (18). This heating and cooling arrangement can be disposed on as many sections of the extrusion cylinder (1) as desired and makes possible an individual cooling or heating of each section of the cylinder, which fact is important for very rapid extrusion processes.