The device of the press (1), for the pressing fruit, and more particularly of grapes. It comprises, downstream of the pressing operation, at the level of the evacuation means of the wort, a chamber (2) comprising a bottom (20) arranged in the extension of said evacuation means and upstream of the transfer means of the wort to storage means, said bottom (20) being associated with cooling means (3, 30) designed to be able to cool the said base on which there flows the must or wort.