44C! omg! They are still alive?
What size is your tent? To tame a 600w hps's heat you are gonna need a enclosed lamp reflector with extraction ducting on each end. The light bulb is enclosed inside the reflector. On each end of the reflector there will be 4" or 6" flange (whichever size you chose) for ventilation hose to be mounted. You can draw in fresh air from outside to pass through your reflector and then out to another part of the house, or route it back outside. I would run it elsewhere in your house because then you can utilize the lamps heat to heat your home.
Or, have your carbon filter mounted in the ceiling of your tent. Tape your extraction fan to the flange on the filter, tape on your dryer vent hose to the other end of your extraction fan, and curl your ducting around 90 degrees and tape it to 1 side of your light reflectors ducting flange. Then tape dryer hose to the flange on the other side of your reflector, and then route the exhaust to another area of the house.
OR, get yourself a LED light that is the appropriate size for your space. Never buy a light based on it's Veg foot print. Always go by the flower foot print. My light is a 8 bar and it says it's suitable for a 6x6 veg space, and 5x5 for flowering. Well, i have mine in a 4x4 tent and it fits perfectly wall to wall.