A device for implementing a method of sizing a cylindrical part following shaping, by plastic deformation, of a metallic material that has maximum structural shrinkage at a maximum-shrinkage temperature between a first temperature and a second temperature, which is lower than the first temperature, is disclosed. The method includes placing the part in a shaft furnace, heating the part to the first temperature, lowering and fitting into the part an internal-sizing tool with an outer diameter greater than an inner diameter of the part at maximum structural shrinkage, transporting the assembly formed by the part and the sizing tool to a tempering vessel, cooling the part to a temperature below said second temperature, and extracting the internal-sizing tool. The method applies to the manufacture of turbomachine casings.