How do you know how an old slab on grade is constructed? I don't know how thick it is, whether it's insulated at all or sufficiently. Could the sills be bad underneath, etc.? You want to know all that when doing a total renovation. I don't know if it should be ripped up and a new insulated slab laid because of this, or if it's possible to go with a mechanically ventilated floor with underfloor heating on top. Building height is critical. Only about 30 mm extra. House: 1800s in brick.