want the op to know there are differences between "inline" fans. I would have one inline 6" booster fan where you pointed to, if possible 5 feet away from any bends in ducting, then where your "inline " is , have a 6" centrifugal inline fan , again 5' away from any bends if possible.
89F would be okay for growing with co2, but definitely not without co2, your yield will be effected.
invest in either an inline fan, or put the lights with just a booster fan on its own loop, then use a centrifugal inline to scrub the air with the charcoal filter, pumping co2 and keeping temps 80-90 optimal
oh yeah i bet you anything if you take the filter off, the room will cool down a ton