The question was how much hotter does it get near the ceiling of a tall room (or not so tall room) as a result of hot airs tendency to rise toward the ceiling and stratify.
I set up a pole and attached thermistor type temperature sensors at 4 places along the pole starting at near floor and going to near ceiling. The sensors were hooked to an Onset 4 channel data logger, and a full day of temperatures were recorded -- see plot below.
The pole with 4 temperature sensors taped on.
The logger and lowest temperature sensor.
Data logger plot -- Red is near the ceiling , blue near the floor, rest in-between. The temperature difference from floor to ceiling is only about 3 F.