And why just the floor? A combined radiant heating/cooling system is best applied from a ceiling- no furniture or floor finish masking to deal with, a fully exposed radiant surface. I trust you've done some internet searches- there is a ton of material out there on radiant cooling system design.
One key fundamental issue you have to keep in mind is that radiant heat transfer is very different from convection (air) heat transfer and you cannot equate the two. "Air conditioning" is just that- "air" conditioning, while radiant heat transfer works by direct heat transfer from your body to the radiant surfaces around you. Radiant heating and cooling is a sensible temperature control function and any latent control has to be done by the air system (DOAS).
I've designed many radiant cooling, as well as radiant heating/cooling systems, and it is a well known and widely used system in many parts of the world.