I wonder the same thing. If you get a chance, try to test the various configurations!
I would suspect you will also see different results depending if you have multiple windows or just 1. For example, if you have more than 1 window and can seal the opening except the fan, then the fan will move x amount of air in or out and will have similar results.
Simply mixing the air inside the room seems like it's probably the least effective because it will result in very little heat exchange at the windows themselves. However, making the temperature within your house more even may make it more comfortable on the average inside your house.
I would suspect you will also see different results depending if you have multiple windows or just 1. For example, if you have more than 1 window and can seal the opening except the fan, then the fan will move x amount of air in or out and will have similar results.
Simply mixing the air inside the room seems like it's probably the least effective because it will result in very little heat exchange at the windows themselves. However, making the temperature within your house more even may make it more comfortable on the average inside your house.