I run a ceiling fan over my stairs while simultaneously running the air conditioning in order to help move the cold air upstairs. The thermostat is downstairs, which isn’t impacted by the hot sun hitting the roof. It may be pleasantly cool downstairs, while it’s still unpleasantly hot in the bedrooms. The fan helps to circulate the air between floors.

Obviously this has nothing to do with running a fan in a closed room. That’s generally silly.