9X8 space with partition

Two chambers
4.5'X8'

Veg gets intake air from floor vent central AC.
Will vent air throu the partition to flower chamber
Veg will. Have HOT5 2x2 16 bulb running 8 bulbs for mums and cuttings. On a shelf. And 2 2x4 HOT5 8bulbs for actuall veg space..

All help us awesome

Oh yea the flower. Wil be running an led cob not so sur really i wil post pics.. A friend. Built it
Also have option for window unit on flowerside..
Or i got a portable unit too
Out take from flower will go intoadjacent room throu wall and filter in its way out...

K so thats it

What is your question?

Best way to cool the flower area.
And control humidity

If intake from veg that has central AC running to it wont work