If moisture is leaving through the top entrance, isn't any extra warmth at the top going with it?
Of course it does but like in human houses, there must be some ventilation that you get fresh air.
If the hive has 25 kg food stores, it generates 10 litre water via respiration. How you get it out is ventilation and condensation.
Cold air has quite few water vapour. When that is heated up, the air is dry and it catches moisture from the hive. Then warm air comes out, like from your lungs, and it makes mist, because cold air cannot keep so much moisture. In our climate we get ridd of moisture with heating, not adding ventilation.