It actually evaporates better with the door closed because of the trapped heat...:)
There is an easy test. Put in a dish that holds a bit of water on top of it. You should find that the water will dry off better if you leave the door closed because the dishes remain hot longer. If you open the door the water on the dish will remain much longer. Try this. Wash dishes in the evening. One evening open the door and check the dishes in the morning. Do the same with the dishes but leave the door closed. The dishes should be dryer in the morning if the door remains closed.