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Yes the floor will be warm to touch, it has to be in order to produce the heating effect.
Many years ago I was installing a lattice of resistive heating cables that were directly encased in the 2" thick floor screed.
The same system is still being used in some installations that of course use off peak electricity, the floor screed heats up during the charge period and emits the heat during the power off time, in some cases when you got to the evening when using the room all the heating effect had been used so you needed an additional heat source.
Most underfloor heating currently used is the wet system where loops of ususlly high temp plastic tubing is buried in a sand and cement screed. It is normal to control the flow of hot water by using a motorised valve controlled by a room thermostat, the heat source feeds a manifold where numerous circuits can be tapped off, each having it's own controlling stat and motorised valve.
In all similar installations heat is never instant, it can take several hours to get the screed to a reasonable temperature to raise the room temp, unlike a wet radiator ststem which can be piping hot in around 20 minutes.
Emgee