Assuming that the second story floor has the same dimensions as the ground floor - 60' x 50' - you can put no first floor ceiling in and you will still be at your dilemma.
There are three modes of heat transfer. In order of greatest to least motive force they are conductive, radiant and convective. Conductive is actually touching a cooler surface to the warmer surface. Radiant is such as the heating elements in your concrete floor. Convective is the gentle flow of air from the warmer area to the cooler area. This is the "warm air rises" concept.
In your situation radiant heat emanating from the warm concrete morphs into convective heat transfer that warms the bottom story. However, once the warm air rises to the bottom of the second floor, it has consumed all of its motive energy to transfer a substantial amount of heat through the second story floor, such that the second story air space is warmed. Said another way, warm air rises, but it cannot penetrate solid objects like the first story ceiling - insulated or not.