What to do about a two story foyer that has a small footprint so it's more like an elevator shaft?

I have forced hot air heating. In the summer, the air conditiner works continuously but the upstairs remains hot where the air collects in the hall at the top of the stairs. In the winter, the downstairs is cold because all our the hot air ends up in the upstairs hall. Will I benefit from replacing my foyer chandelier with a ceiling fan? Any drawbacks to this?