How to set up CO2 for a closet grow

I'm growing in a 5 x 4 x 10 foot closet. Right now I have one 2x4 flood table and I plan to add another with a 600W light over each table. The lights are air coolable and the only opening in the closet is a 2 x 8 doorway.

Its a small space (~200 cubic feet) so I figure I'd seal the doorway and have ducting bringing air from outside the room, throught the sealed doorway, through the lights, and back out of the room. That way the air running through the lights would not afftect the rest of the air in the grow room (right?).

I have a wall mounted fan circulating the air in the grow room. So, if I had all of that ducting set up would I just be able to release CO2 (to 1500ppm) in the sealed room and watch my plants love life?

at some point the heat buildup will require you to vent the room. you will still need an exhaust for the room. ive seen lots of co2 growers that have a thermostat that kicks the fan on when it hits a certain temperature to bring down the heat. they have it rigged so co2 shuts off when the fan is on an then come back on as soon as the fan brings the room back down to ideal temperatures

Would the ducting I mentioned runnning through the lights not keep the temperature down enough? I was assuming that if I aircooled the lights it would be enough to keep the closet the same temperature as the room that it's in. I plan to have that vent sucking air from outside the room, through the lights, and back out of the room so I assume if I did that right it would have no effect on the air inside the closet other than preventing it from getting hotter.

how much do those thermostats that kick on the fan usually run? and are there regular outlet ones?