"fan" button On AC thermostat?

That's not really how it works.

The Fan ON position only keeps your blower running, but unless yours is a relatively new house with tight construction and a whole-house makeup air system, the AC blower really just moves air from inside the house, through the HVAC system, back through the house. It helps with filtration and keeps the air circulating, but doesn't do much about moving air from outside to in.

If you have a makeup air system that helps move fresh air in from outside, it's going to have a heat exchange system to help minimize heat losses.

For best results, find a window on one end of the house to place a fan into - preferably on the north or eastern end, where it will be cooler, and another window on the opposite end to leave open. Have the fan be blowing INTO the house, not pulling out. You don't want to create a negative pressure environment that can cause a gas water heater vent to backpuff into the house, or pull in unpleasant smells through the fireplace chimney. Modern construction and equipment should prevent such problems - but nothing is foolproof, and why go looking for trouble?

To make the most of the effects of this, at some point you do want the HVAC blower to be on, to help mix the fresh air throughout the house. But if you don't have to, don't leave it on all night. Thirty minutes or so at the beginning of the evening and another half hour in the morning does a pretty good job of starting the house of with a full charge of fresh, cool air before you have to seal things up for the heat of the day.