a cylinder 4 5 the conveyor 28 is rigidly attached to the motor 6 and to the central body 3 by a plurality of fastening elements 34 of which one is illustrated in fig1 as illustrated in fig5 the compressor unit 1 comprises an intermediate cooling part 35 for cooling the compressed air exiting the first cylinder 4 before it enters the second cylinder 5 which forms the second stage the intermediate cooling part 35 comprises a tubular 36 pipe for the passage of the compressed air the pipe extends along a curved trajectory t and close to the central body 3 and the electric motor 6 outside them for a stretch of the curved trajectory t the tubular pipe 36 comprises two tubular portions 37 38 through which the compressed air exiting the first cylinder 4 runs in parallel the two tubular portions 37 38 into which the pipe 36 is divided advantageously allow an increase in the heat exchange surface area of the pipe 36 improving the cooling of the compressed air the intermediate cooling part 35 is at least partially inserted between the motor 6 and the conveyor 28 the first and second ventilation parts 22 25 the conveyor 28 and the intermediate cooling part 35 together form cooling means 39 for the compressor unit 1 in practice during.