Having grown up in a hot place (Australia) - we think about ventilation a lot. You're right - cross ventilation is really important. Generally you want to pull

Having grown up in a hot place (Australia) - we think about ventilation a lot. You're right - cross ventilation is really important. Generally you want to pull air in as low as possible as it's cooler. And then push out as high as possible. As "cross ventilation" somewhat implies, usually this is across a room or building for the best airflow. A fan in a regular-height window and an open vent (a higher window, door louver) generally works pretty well. Even if it's the same window, it'll work ok.