The sleeve roll according to the present invention has the metallic sleeve 5 fitted over the rubber roll 4, covering the surface of the shaft core part 2, and can be efficiently heated or cooled by having the passage P formed between the metallic roll inner tube 2a and the metallic roll outer tube 2b for the thermal medium to flow through. It also has the heat conductive material 6 mixed into the rubber roll 4, so that it has excellent heat conductivity and the surface of the sleeve can be quickly and efficiently heated or cooled, thus preventing the material to be formed from sticking to the roll.