I have a couple of rooms that are functionally a fully-enclosed 2nd-floor balcony, with a concrete beam + breeze block system as the base, and floor tile cemented directly over that (no insulation that I'm aware of). I want to add radiant heating (water-based), but I don't have space to add it above the concrete - raising the tile would cause the floor to be above the level in the rest of the house, and the interior doorways have limited height as well (solid granite lintels, not feasible to open upwards).
My plan is to add a couple of inches of insulation to the exposed underside of the concrete before next winter, and I'm wondering how effective it would be to attach PEX-style tubing to the underside of the concrete before the insulation.
I can't find anyone who has attempted this before, but I'm wondering if it is a reasonable idea, and what the potential pitfalls might be. I assume it's going to take a fair bit of time, but that it will eventually heat all the way through the concrete - or am I going to lose all my heat downward and out despite the insulation?
These thermal images are from the energy certification 5 years ago, before the windows were replaced with double-glazing (apologies for the google translate):



