To help with high temps and keep it on the downsie, I suggest buying 2 4" inline duct fans. Even booster fans will work on something that small. Great thing about them are 1) cheap, 30 bucks each 2) quiet 3)can be wired into a 120v outlet 4) super quiet.
Now what I would do is buy a reducer for the duct fans from 4 inch to 3 inch. I would do this because it made it easier to mount, and easier to DIY a carbon filter.
So the shelf that divides the veg/flower rooms is an airflow block assuming you will place an intake fan at the bottom, and outtake at the top. I would cut 2 3" holes at the back of the shelf. Buy$ 2 3" abs pipe 90's and glue them into the holes. duct tape them to prevent light leaks, and place a black stocking over one end and now you have full ventilation