For 6x6 I think you need 4x600W to properly cover, particularly if you want to grow larger plants.
Think about it for a minute, a 600W covers 3x3 well, 1000W covers 4x4. If you use 2x1000W, you'll definitely need a mover and the outer edges will suffer somewhat. 2x600W will only cover half the room.
To control the heat you will need to aircool the lights. An 8in. Vortex should do the trick, then a 6in can handle the movement of fresh air into the room while it also removes any remaining heat. Except for the hottest months of the year, you can do without the AC unit. Make sure you have one just in case. 15k BTU should be big enough. Eventually you can eliminate the exhaust with the addition of CO2 injection. Then the 6in can sit in the corner recirculating through the filter.
Just my .02
Fred