The screed does not emit cold but absorbs heat and transports it to the heating system.
There, the heat is transferred to the medium (brine or air) via the heat exchanger.
which only works if the medium is colder than the heat from the house. Otherwise, we are talking about active cooling.
But: air is known to be a poor heat storage medium. If I place a heat conductor on a 60°C warm steel, it quickly becomes 60° warm; if I blow 60° warm air onto it, it takes a long time. So how does the room efficiently transfer heat to the floor?