In order to permit more effective cooling in comparison to the prior art, in particular in its floor area, of a hollow glass article (1) standing upright on the base (2) of a setting plate (4) provided with transcurrent orifices (9, 9′, 9″) forming a cavity (8) between a base (2) and the facing surface of the setting plate (4) of the standing surface (2″), it is proposed to utilize a part of the orifices (9) situated inside the standing surface (2″) for the supply of cooling air into the cavity (8), and to utilize the remaining orifices (9′) inside the standing surface (2″) only for the extraction of cooling air from the cavity (8). By configuring the orifices (9, 9′) that are utilized in each case for the supply and extraction of cooling air into and out of the cavity (8) so that they are at least approximately cross-sectionally identical, a throughput of cooling air through the cavity (8) and thus the available cooling performance can be varied within broad limits, but in the absence of an adverse effect on the stability of the hollow glass article (1) or a resulting risk of uncontrolled positional displacements on the setting plate (4).