A 4" fan hooked to a 4" carbon filter won't ever realistically exchange enough air to help you manage heat in a 3 x 3 x ? space. Why?, because for one, all booster fans are way over CFM rated, yes, some get to 80% of their stated CFM rating but most only provide 70% to 75% of what their stated CFM rating is. But say your fan is one of those that actually hits its CFM rating, it still wont realistically help you manage heat in your space if you are not exchanging the air in your space at least (3) times a minute, and a 145CFM rated fan by its self can barely do that when used in a 3 x 3 x 5 (or greater) area. 3x3=9x5=45x3=135CFM. So if your area is a 3 x 3 x 5 and your fan is rated at 145CFM(s) without the carbon filter your fan will barely be able to help you mange heat in a 3 x 3 x 5 area. But again, I have never seen a booster fan pull or draw over 80% of its stated CFM rating. Then secondly, when you hook a carbon filter up to a fan you will lose 20% to 35% of the fans CFM rating by way of a negative pressure restriction if the fan pulling air through the carbon filter does not at least match the rated air flow value that the carbon filter is rated at!
Anyhow... I have found that a 4" carbon filter is perfect for a 3 x 3 x 4 (or greater) space, but there isn't a single 4" fan hooked to a carbon filter that will realistically help one mange heat in that space, but you can fix that simply by using a 6" fan with at least a 240CFM rating hooked to a 6" to 4" reducer, that is then hooked up to your 4" carbon filter!
