Heat exchange in an open stairwell

It's a hot day today, AC was on downstairs, AC upstairs was off because there was no one up there.

My question is, why is the change in temperature at floor level of the second floor instead of, say, the bottom of the stairwell?

When climbing the one flight of stairs, when your head starts coming above the hallway floor you get punched in the face by the heat.

When descending the stairs (barefoot), feet get cold as soon as they dip under the level of the hallway floor