CO_2 to deal with heat?

Alright, I have 2x4x6 closet, and I'm having trouble keeping the heat down. I already started flowering, so I don't want to change the fans out or anything until later, but the good news is it's about 66F outside right now. With the doors in my apartment closed, my 600watt light heats up the apartment to 77 degrees and it gets to about 86 degrees on the inside of the closet. I'm expecting the weather outside to not get much higher than 70 degrees for the rest of flowering.

I'm thinking the quickest/easiest solution to this problem is just to add CO_2, and then, after flowering, I can change out the fan and work on the box a bit to keep the temps closer to the temp inside of my apartment. I figure with little effort during the summer it'll be between 80-85 degrees w/o needing an a/c.

If I go this route, will bottles with yeast in them be sufficient? It seems like a CO_2 tank is excessive for a 2x4 closet, but if it's needed, it sounds like it'll be a good investment.

oh and I forgot to add that I can't leave the window open because of my neighbors and bugs. I left them open for about 5 days and then I got an infestation of fruit flies... I have a screen and everything, but the little shits are so small they can get through it. It's in my crop, and they're really annoying flying around my apartment. Anyways, I'm doing the orange juice + rum thing and have flying insect strips, it seems to be working. I just don't want to deal with this stuff for 8 weeks.

BUMP

I've heard that adding CO2 alone actually raises the temp... Is this true?

i read that, with the proper amount of c02 in the room, u can have the temps up to 85 and maybe even hotter and u can even have the light closer to the plants

I heard that just adding CO_2 to a room will cause the temp to go up? Is this true?