An injection blow molding machine (10) having a core rod (18) against which a parison of a thermoplastic material is formed by injection molding. The core rod is cooled by causing a stream of compressed and conditioned air from an inlet manifold (52) to flow through the core rod. The core rod has an outer annular tube (70) surrounding an inner annular tube (74) and defining an annulus (80) therewith, and the annulus (80) is divided into inlet and outlet flow passages (82, 84) by opposed projections (76, 78) that extend thereinto. Spent cooling air from the core rod is exhausted to an outlet manifold (54) from which it is discharged to atmosphere through a line (42) or recompressed by a compressor (46) and returned to the inlet manifold (52) after reconditioning. The conditioned air has a regulated pressure as a result of passing through a pressure regulator (24), and is heated, if needed, by passing it through a heater (26), or cooled, if needed, by injecting a water spray from a spray nozzle (36) thereinto.