PROBLEM TO BE SOLVED: To prevent a material to be formed from sticking to a sleeve surface by using rubber having satisfactory thermal conductivity thereby enabling the sleeve surface to be highly efficiently and quickly heated/cooled.SOLUTION: A sleeve rubber roll 1 is formed which is obtained by fitting a sleeve 5 over a surface of a shaft core part 2 which can be heated/cooled, via a rubber roll 4 and by mixing a heat conductive metal 6 in the rubber roll 4. The shaft core part 2 is formed by forming a heating and cooling medium flow passage P between a metallic roll inner tube 2a and a metallic roll outer tube 2b. An offset prevention device 11 using tension springs 12a and 12b is provided between the shaft core part 2 and the sleeve 5 so that the offset of the sleeve 5 with respect to the shaft core part 2 is automatically repositioned to its original position. When the sleeve rubber roll 1 is manufactured, the rubber roll 4 in which the heat conductive metal is mixed is formed, the shaft core part 2 in which the heating and cooling medium flow passage P is formed is inserted in the rubber roll 4 and then the heated and expanded sleeve 5 is fitted over the rubber roll 4.