I have a 3'x4'x7' closet. Likewise, I cannot drill, or other wise make holes in the walls or ceiling. I have a duel window fan positioned on ladder, in front of the AC, blowing cool air from that region of the room, downwards toward the open closet door. I have no intake fan, other than the aforementioned one, and there's an oscillating fan positioned toward the back of the closet, blowing air under the lights, over the tops of the plants, and out the door. The AC isn't always on, but the fan remains in the same position, and works well as long as the air is cool.
With a ghetto setup, you'll encounter engineering challenges. Besides the timer that turns lights on and off, there's nothing automated about my grow. Climate control is manual. As for humidity, with a constantly opened door, it's at the mercy of the normally dry apartment air. The current temperature and RH are 83 degrees and 33%, respectively. With the AC running, it's even cooler.