A fan would be fine. The key to good ventilation is the air has to flow. Either low to high or side to side. From what I can see in the picture, the size of the opening in the door should be adequate. If you can add a similar size opening in the opposite corners you would have good cross flow. If that size is not compatible then a couple of smaller vents (1 foot square min) as high on the opposite corner will be better than none. If the opposite side is the outside of the barn you can install some Gable end vents for attics to make the openings more visually appealing and weather resistant from the outside. They are relatively inexpensive and easy to install. Hope this helps.