an apparatus for cooling a transfer mandrel on whose top portion a thermoplastic resin parison is mounted and which is rotatably engaged with the peripheral portion of a rotary table . the apparatus is arranged along the peripheral portion of the rotary table adapted to rotate oppositely to a heating means . the apparatus comprises a cooling block having a cavity through which cooling water flows and a concave surface opposing to the transfer mandrel which has a profile conforming to the cylindrical portion of the transfer mandrel , means for adjusting the position of the cooling block , and a spring which pushes a surface portion opposite said concave surface of the cooling block .