A.Wood parquet tiles can be installed over a radiant slab with reasonable success. They are relatively thin, and can be bedded in solid mastic adhesive. This provides good heat conduction, and prefinished parquet tiles are usually well dried, so shrinkage is minimized.
Floating hardwood flooring, which is installed over a foam pad, also might work. However, the more insulating material you install on the radiant slab, the higher the temperature of the slab needs to be. I have seen problems where the higher water temperature needed to compensate for thicker wood flooring or carpeting has made the floors...
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