yes. You will notice auto repair shops running the office AC and blowing it into the bay, even in really small bays like your barn. Best if there is a roof vent that can let the hottest air out, but the walls and ceiling of the barn will be as big of a heat sink as the AC blowing hot air, but I would keep a window wide open or the door cracked. you will have power to plug into I assume, so at worst the compressor will just run more. Somehow people in 120 degree deserts still run their ACs with some cooling effect.