My business has a swamp cooler (evaporative), but none of the windows open so I have no way to vent air. There is a vent in the alcove (?) over my front door facing downward. The vent is about the size of a box fan. I have been thinking about putting one face down on top of the vent.

If this is not a good idea is there a better option? I have an outlet not too far from the area, but do not think that there is anywhere near to hard wire. I could run a wire out the vent for a solar panel, but the awning is north west facing.

Vent opening:

With fan laying on top: