“Cold pressed” is a marketing label description for olive oil not really cold produced by continuous centrifugal presses.
Today the paste is almost always warmed during the malaxation** process, before being centrifuged, using horizontal decanters (Olives are harvested in the winter when it is cold).
According to IOOC regulations this is still considered “cold pressed”.
Heating the paste during malaxation will extract more oil but will hasten oxidation, anyway most of the producers are interested in extract more oil and reducing time by overheating the paste.
** Malaxation, is the action of slowly churning or mixing milled olives in a specially designed mixer for 20 to 40 minutes.