The aerator in question is on this photo, there is an identical one which extracts from the kitchen towards the bathroom placed on the opposite wall.
Since the hot air is always high, and it makes a practically direct circuit from one wall to the other, that is to say a direct breath on the false ceiling cooled by the metallic structure which is in contact with the walls outside (cold).
Hence the traces of humidity on the areas bordering the metal structure.
Not being at all professional can you help me by validating or denigrating this theory?
Thank you in advance