That fan will want to see more than a 4" intake hole to reach max flow. Maybe like three or four 6" intake holes. You would have to dial it in.
OK depending on the carbon filter, it may be stealing a lot of flow, or it might be a high-flow version. But the ducting heading out of the fan, that all sounds very restrictive.
So would removing the carbon filter help lower the temperature. Iām also not really worried about small since the exhaust is on the roof.
Well the carbon filter is most likely restricting some flow. Maybe a lot. But the 4" to 2" reducer on the exhaust is killing you. You want the exhaust tubing to be as short as possible, & at least as wide as the fan exhaust opening, & with minimal bends in it.
Then youāll still need to ditch the intake fan & give the tent more intake area to let the 6" exhaust fan reach max flow at 100% power.
You can tune the intake area with the carbon filter in place, but if the carbon filter is restrictive & you remove it after tuning the intake area, then you would want to go back & re-tune the intake area by adding yet more intake area. Ultimately you want to tune it so that the tent has a little negative pressure on it. Keep adding intake area until you lose negative pressure - tent stops sucking in. This means the fan is right around max CFM, accounting for any restrictions that may still be there. Then fine-tune it by taking a little intake area away to keep a little negative pressure on the tent, in order to keep a little velocity on the intake air, & to try & help keep smell in.
How hot is the air going into the tent?
If you want a visual reference, you can make a swing gauge for the fan & bench flow it, & then you can see how lossy everything else is as you add them on. You can also use the swing gauge to dial in the intake area more easily.