A hot-beverage-making apparatus, in particular for milk beverages such as cappuccino, chocolate and the like, comprising a container extending along an axis, a lid closing the container, a rotary mechanical stirrer fitted with an impeller, and a steam wand connectable to a steam source and having an end steam outlet. The stirrer and the wand extend, sloping with respect to each other, inside the container, and the end steam outlet of the wand is located above and radially eccentric with respect to the impeller of the stirrer.