An apparatus including a container (2); a removable cover (3); a rotating stirrer (6) which extends inside the container (2) and is provided with an end impeller (8); an electric motor (22), for driving the stirrer (6) via a coupling joint (9, 10, 23, 26); and a hot steam dispensing wand (13) extending inside the container (2) and connectable to the steam source (52) of a coffee machine (CM) via a connection union (12) associated with the cover (3). The electric motor (22) is contained in a housing (21) which is separate and distinct from the cover (3) and is connected or able to be connected to power supply terminals (49, 50) with which the coffee machine (CM) is provided. The cover (3) supports the stirrer (6) rotatably and the inlet fluid connector (12) thereof is directly connected to a steam dispensing fluid union (48) of the coffee machine (CM).