My question: Am I saving any energy by setting back the thermostat for
that


Not knowing the ambient outside air, the insulation and a bunch of other
factors it seems to me that anything here is a wild assed guess.

Guessing you might try waiting another hour or two in the morning for the
sun to help out since this is a southern facing exposure. Of course if your
having a blizzard that day, the sun will not help much. Heating a slab is
slow business. Let alone the room.
Keeping the door closed at night certainly will help a bit.

Last time we had this sort of discussion, this was the
consensus. (It was water-heaters, that time)

You don't have to guess. The amount of heat the slab and the
room pump into the rest of the universe is proportional to how
warm they are. If they are cooler, they will pump less
heat into the universe. It will *NEVER* take more energy
to heat the slab back up than it would have taken to
keep it warm in the same environment in which it cooled.

So unless you're using a more expensive heat-source to
re-heat than you were to keep it warm*, it is always
cheaper to set-back.

--Goedjn

*(this is the gotcha for electric heating, if your
electric co has variable prices by time-of-day)