Keeping floor warm without overheating the room will physically not be possible (at least in a somewhat mondern house... or well... if you open the windows or turn on the AC or something it might work, but not recommended).

Most of my house has a ceramics floor. Bedrooms have vinyl and that feels a lot softer/warmer to the Touch even if the floor heating isnt on.

I do not know how houses are build in your region, or what alternatives are reasonable on the market, but in my area 100% of the houses in the last years are floor heated.