A device (1) for grinding roasted grains, in particular coffee beans, of a kind including a grinding chamber (9) in which one or more electrically operated grinders grind coffee beans in order to reduce them to powder. The grinding chamber of the device is equipped with a plurality of cooling fins (29) that assist in removing heat produced during grinding, without the need to use cooling fins or similar cooling devices. Thanks to the provision of the cooling fins (28), the device (1) is inexpensive and compact and avoids an excessive increase in coffee temperature during grinding, thereby preserving the organoleptic qualities of the coffee.