No door on the closet might be a problem. See what you can improvise to close the space. Keeping it lightproof during flowering will be crucial, so you'll have to close it somehow... You can make a passive exhaust with as little as an exhaust fan up top and an air inlet down low to keep cool air comin in. If odor is a problem you might have to invest in something a little more extensive.
Whats your setup? Be more specific and it will make it easier for us to understand your situation.
Good luck, now its time for you my friend to get those creative juices flowin'.
