A system for air conditioning at least one partial region of an aircraft comprises an air providing device for providing air to be supplied to a region of the aircraft to be ventilated at a desired temperature and pressure. A supply air duct is connected at a first end to the air providing device. A second end of the supply air duct is connected to an air inlet which opens near the floor into the aircraft region to be ventilated. A control device is set up to ensure that the air provided by the air providing device enters the aircraft region to be ventilated via the air inlet at such a speed that the air is distributed near the floor in the aircraft region to be ventilated and rises at heat sources present in the aircraft region to be ventilated, and that the air provided by the air providing device enters the aircraft region to be ventilated via the air inlet at such a temperature that a desired ambient temperature is set in the aircraft region to be ventilated.