If you have cool nights, setup fans up at night to bring the house down to a lower temperature. Close everything up in the morning when the outside temp starts rising above your inside temp. If your place is insulated reasonably and there's no excessive sun from windows, it will stay cool for the day.
Protip: Setup the fans in all rooms on one side of a chokepoint in your house/apartment (stairwell/hallway) to exhaust, to encourage airflow. Open up all the windows on the other side for intake. It'll also help reduce pockets of hot air left over from the day before.
I practice this same thermal battery idea as well with an extra tip of having a couple of fans on timers (sun up to sun down) that sit on the floor and blow the cold air up. It makes a significant difference, especially if you can sit a fan where the cold air from the AC falls to the ground.
Pro tip: Point the fan so that it blows outside and DO NOT put it directly on the window or right next to it. Instead, move it ~50cm away from the window to take advantage of Bernoulli's principle (push the air out more efficiently by pulling the air surrounding the fan).
You can cool down the room even if the door is closed. You are lowering the pressure inside your room so the outside air is forced to rush in. If you place the fan like I explained, and point it at the lower part of your window and you put your hand next to the upper part of the window, you will feel the cold air coming in.