The device has a steam extraction air path for connection to an air outlet channel leading out of a room into the outer atmosphere. The air path contains at least one fan generating a steam extraction air flow and at least one odor filter. A cooling air path has at least a second fan generating a cooling air flow. The odor filter is arranged in the steam extraction air path downstream of a heat exchanger for exchanging heat between the air paths. The device has a steam extraction air path (3) from a room (12) containing the device for connection to an air outlet channel (32) leading out of the room into the outer atmosphere, whereby the air path contains at least one fan (2) for generating a steam extraction air flow and at least one odor filter (4-2), at least one cooling air path (5) with at least a second fan (6) for generating a cooling air flow and at least one heat exchanger (8) for exchanging heat between the air paths. The odor filter is arranged in the steam extraction air path downstream of the heat exchanger.