The thinnest floor heating systems are electrical: the wires that generate the heat are thin. Warm water systems have to be thicker because the pipes are thicker. Normally, you lay down the insulation, put the pipes on top, and cover the whole lot in a good thickness of concrete skim.
Here is a picture of the system planned for my room, that is a little different. The grey polystyrene provides the insulation, and offers channels for the heating pipes. However the pipes are cradled within steel heat conductors that wrap around the pipe and conduct the heat evenly across the surface. With this method you can use a thinner layer of concrete on top, and the whole thing only takes up a few centimetres.
The trailer? The fridge packed up, so it's carrying a new fridge.