The present invention relates to an apparatus and a process for subjecting oleaginous vegetable material to a continuous prepressing for extracting at least part of the oil contained in said oleaginous vegetable material and producing a cake comprising an at least partially de-oiled oleaginous vegetable material. The apparatus comprises a mechanical prepress for mechanically compressing said oleaginous vegetable material, wherein the prepress is provided with a cake discharge for discharging the cake to a cooler. The cooler comprising means for subjecting the cake to a downward movement, and means for supplying a coolant gas, preferably air, in a counter-current flow to the downward movement of the cake with the purpose of cooling the cake.