Fan/light/heat/small space question

The grow tent is an unfamiliar size, at 2x3.5x4. I've got a 400w ML (cool tube) and a couple of the 26w high output cfls for veg. The space gets really hot so I've ordered a 4" centrifugal fan and carbon filter to aid my 6" duct booster I'm already using. My question is what would the best way to hookup said system with having the best results?

As it is right now I have the 6" duct booster blowing room temp air through the cool tube and outside the tent. Should I just add the centrifugal and filter and leave light setup as is for two exhausts? One through the light and one through the carbon filter? Or should I have a passive intake for the light to breath cool (outside tent) temp on the light itself.

Main reason I want to make this work a bit better is because I don't have a super thick canopy as the tent only stands at 4' high. The light is more than enough, but I want to get it closer to the canopy, because I know I can get it closer but I really want to be sure I can maintain heat problems.

I live in the far north and the house temperature maintains at roughly 19 degrees. The tent temperature is roughly about 34 degrees at worst

Just in addition: I like the temperature the canopy gets as it seems like an almost perfect conditions, I really just want to maintain those conditions with having the light closer. I also have 2 5" clip on fans blowing either way on the canopy to disperse the heat down as well. Roots usually maintain 19-21 degrees in the reservoir. Thanks again guys this is my first post on this site.

When you say you got the 6" duct booster fan blowing room temp air through the cool tube and outside the tent:

Do you mean you are sucking air from outside your grow tent through the cool tube, and then back out of the tent?

Are you moving any air through the grow box itself?

No it is being sucked through the light and outside the grow tent. But it still does not seem like enough ventilation, I was thinking I could run the light exactly like you said and just add the 4" fan/filter combo in addition. Let me know what you would prefer and why.

That 4" centrifugal fan is probably stronger than the 6" booster fan.

So I would

- put the filter right in front of the 4" centrifugal
- hang that filter/fan combo into the grow box with those bicycle rubber bands (avoids vibration)
- Let the 4" filter than push air through the light and outside of the tent.

- Use the 6" fan to push air into the tent at the bottom.

You cannot put 2 fans directly behind each other. That somehow doesn't work properly. Its better to have one suck air out and one push air in.