"Well, he told me that the screed upstairs is drying out too much and thus the moisture can no longer escape from the lower layers of the screed."
In my professional career, I have had to listen to a lot of nonsense.
This statement is just adding to that!
As long as a porous component, and a mineral screed belongs to that, is not surface-sealed, the water vapor pressure within the screed structure is always in correlation with the vapor pressure of the room air!
Regardless of how thick the screed is.
However, it can never be advantageous for a building if it is not heated during the cold months!
Gypsum-containing as well as cementitious building materials react to high relative humidity by absorbing moisture, which is reduced by heating the rooms.
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Regards: KlaRa