A machine for heating a food substance, such as milk or a milk-based substance, as a standalone machine or as a machine incorporated in a food processor such as a beverage maker e.g. a coffee maker, such machine comprising: - a container delimiting a cavity for containing said food substance to be heated, such as a container that is mechanically and/or electrically passive and/or that has a side wall and a bottom wall for delimiting its cavity, the container being optionally: - generally cup-shaped or bowl-shaped or cylinder-shaped wherein the sidewall is generally upright and the bottom wall is generally flat or curved; and/or - provided with a thermally insulating outside material (10") and/or with a handle, for seizure and optional displacement of the container by a human hand; - a module comprising a housing means that contains an inner chamber (22,22a) and that delimits a seat, such as a generally planar or cylindrical or cup-shaped seat, on or in which the container is mounted, such as removably mounted, the chamber (22,22a) containing one or more electric components (23,24,25,26) comprising a generator of an oscillating electromagnetic field directed to the container for heating said food substance in the container, at least one of said one or more electric components (23,24,25,26) radiating heat within the chamber (22,22a) when electrically powered, such as heat generated by an electric resistance of the component (23,24,25,26), optionally the one or more electric components (23,24,25,26) including at least one of a control unit and a power management unit, the housing means having a separation section and an outside section (22"') distinct from the separation section (22"), the separation section and the outside section delimiting at least part of the chamber (22,22a), the separation section (22") separating the chamber (22,22a) from the seat, the outside section (22"') being separated from the seat by the chamber (22,22a), characterised in that the separation section (22") and the outside section (22"') have such respective thermal conductivities as to promote an evacuation of said heat radiated within the chamber (22,22a) outside the module via the outside section (22"') rather than into the container via the separation section (22"), optionally the ratio of heat evacuated via the outside section (22"') over heat evacuated via the separation section (22") being of more than 2 such as at least 4 e.g. at least 9. - a container delimiting a cavity for containing said food substance to be heated, such as a container that is mechanically and/or electrically passive and/or that has a side wall and a bottom wall for delimiting its cavity, the container being optionally: - generally cup-shaped or bowl-shaped or cylinder-shaped wherein the sidewall is generally upright and the bottom wall is generally flat or curved; and/or - provided with a thermally insulating outside material (10") and/or with a handle, for seizure and optional displacement of the container by a human hand; - generally cup-shaped or bowl-shaped or cylinder-shaped wherein the sidewall is generally upright and the bottom wall is generally flat or curved; and/or - provided with a thermally insulating outside material (10") and/or with a handle, for seizure and optional displacement of the container by a human hand; - a module comprising a housing means that contains an inner chamber (22,22a) and that delimits a seat, such as a generally planar or cylindrical or cup-shaped seat, on or in which the container is mounted, such as removably mounted, the chamber (22,22a) containing one or more electric components (23,24,25,26) comprising a generator of an oscillating electromagnetic field directed to the container for heating said food substance in the container, at least one of said one or more electric components (23,24,25,26) radiating heat within the chamber (22,22a) when electrically powered, such as heat generated by an electric resistance of the component (23,24,25,26), optionally the one or more electric components (23,24,25,26) including at least one of a control unit and a power management unit,