My heated floors run at about 30°C on a very cold day.

That seens to be normal on a cold day. Your floor heating should be fine. Once the moisture has had a chance to be evaporated, any operating temperature (within its range, of course) for a floor heating system should be ok. I suspect that the problem in the picture is that the moisture has been trapped inside the floor, because the floor tiles sealed it up.

When moisture cannot escape, it goes for the weakest point - in that case the floor surface, because it can't go downwards (water vapor always rises up) and it can't go sideways because of the walls of that room (the screed floor is between the walls). The temperature the floor heating could have been operated with didn't need to be that high, just hight enough to make the remaining water start to change its aggregate state. Water vapor takes up more space than liquid.

The ammount of water that is brought into a buildung with concrete, screed, plaster, etc. (basically all material that has been a pile of dirt once) is often underestimated.