Heat and Venting issue - please help.

I am running a 1000w HPS in a 4x8 walkin closet, with an air cooled hood. I have run some ducting from a window ac in the room, one to the floor to disperse colder air, and one into the hood. I have a medium CFM fan pulling air out from the other side of the hood and venting it out of the closet. My problem is during my pre-flower heat tests I am still hitting 86-88 degrees with the door open. My question is should I run another ducting strip from the ac to the floor of the closet, or should I just use the one that goes to the hood and let the fan just pull hot air out from the hood and closet through the other opening? I also have a DIY carbon filter I tossed together, should I pull the air through that before it goes through the hood and out of the room? I will try to take picture of it but I think I described it well enough.
(I also have three fans going in there to circulate air around the room- my goal is to maintain 75-82 degrees)
Thanks for the help

more cfms to cool bulb . no ac to bulb . ac to closet it self . are you cooling the bulb and getting rid of the heat > you must air cool and get rid of the heat , not putting it back in the room . the AC should then keep the room cool

well right now i got a 600HPS and have similar setup except no AC just humidifier pushing cold air in through my intake. I have the cool tube hooked up to some insulated ducting and i have a Hydrofarm Active air 6" exhaust fan pushing hot air from lamp and grow room out the grow room

my temps are not being nice at all... with everything turned on to MAX to try to cool the grow room down, still the grow up in the day time goes up from 11:00 am morning from 82 degrees to 1 in the afternoon is already 86 degrees!!

im thinking about switching my bulb from 600 to 400 for the summer time... or else its gonna be impossible to grow with over 85 temp is way to hot..

i havent tried to hook up a AC like the one you have a window AC, i was thinking about buying one from walmart, but your telling me its innefective at all at cooling temps in the room? does it even cool the temp down 5 degrees?

Yes it cools the room signficantly, down from over 90 degrees. I have decided I buying a bigger fan today, and just air cooling while having two 4" ducts from the window ac to cool the room itself. Should work great. I am going to use my DIY carbon filter and new fan to pull through the light and out the closet. I think I am ready for flowering next week!

So after a few heat tests with the new fan, I am still running around 85 degrees at best mid-day. Is this going to be too hot to flower a kush variety?

I have a similar closet I am growing in. I put a bathroom vent fan in the ceiling right above the light, and I have a 20" box fan pulling cool air in from the rest of the house. Keeps cool air flowing well. Get the cool air coming in below, and rising through the plants. Take advantage of heat rising.