How do I convince my girlfriend we shouldn't open the windows when it is hot out?

My girlfriend wants to open the windows when it is clearly 10 or 20 degrees hotter outside than it is inside. I tried to explain to her that through conduction the temperatures will equalize, hence making it hotter inside. However, she insists that there is some sort of mystical cooling property of "circulation." How do I convince her there is no benefit to the circulation when it is hotter outside? Or maybe someone can convince me I'm wrong after all.