My little grow room is only 4' tall, and I am running a 400W HPS with a cool tube. I have it on 24/0 right now (for the past 2 weeks or so) and heat doesn't seem to be too much of a problem. My ambient temps stay in the mid to high 70s most of the time. As far as how close the plants can get to the light, it all depends on the ventilation. I think it was GardenKnowm who once said something about how you could put a 1000W up your ass if you had enough airflow. I have one 250cfm inline fan from Lowe's. The glass stays pretty cool, but I wouldn't want any plants to be touching it directly. What you really need to worry about is really getting your LST chops down. My cooltube is 6" thick. Add about 2 more inches for the hooks on the cooltube and the hanging hooks on the ceiling. Take off another 6" or more for pots (I know you are not even considering hydro in this space, right?) and that takes you down right under 2 feet. That is not a lot of room.
So, yes, it is possible. Have you considered a ScrOG? I think this may be your best chance for success.
S-Town