Should I set the heat in the basement to 68, or install a drape system around staircase opening?
Close off the staircase with draperies or whatever. Keep the basement at 55°. Heat will be contained in the basement and at the same time keep the tiled floor warm. If possible close off all stairways, as heat rises the upper floor will be hot and the rest cool. You will not only save fuel but be comfortable. Add Ceiling Fans, they will bring the heat down and cost pennies a month running 24/7.
It depends upon how the basement was finished off and the type of heating/cooling installed. If the walls were properly insulated including the area between the floors you should not be losing a great deal of heat to the outside. Heat lost through the ceiling of the basement or up through the stairwell will only contribute to heating the upper floors. Losses will be limited to the percentage that goes through the walls and what is attributable to heating more space initially. With regard to the last item raising and lowering the temp may work against you in this situation. By describing your unit size by the ton I would assume you have forced hot air heating with an installed cooling coil or a heat pump. If instead you were dealing with a large thermal mass like radiant floor heating reaction time might be so slow that heat setbacks (manual or automatic) might not be worth the discomfort. You would have to anticipate your heat rise by as much as half to one day. Your 12.5 tons of heati