The present invention relates to mold cooling method and system for a glass container forming machine that includes at least one mold holder including mold halves that are movable between a closed mold position for forming the glass article and an open mold position for releasing said article, each of the mold halves having axial passages for cooling each of the mold halves. A support structure having a fixed upper support section and a movable support section. Means for providing a cooling flow are coupled in coincidence with a series of openings in the movable support section. A cooling flow distributor located above the movable support section, the cooling flow distributor having a lower section in coincidence with each of the openings of the movable support section for the passage of the cooling flow and, a upper section in coincidence with each of the axial passages of each of the halves of each mold, the cooling flow distributor being movable between the closed mold position and the open mold position.