I have a little 5 sq ft space that I am putting a 4" centrifuge type fan (with a speed controller) in for flowering. You need a fan like that if you want to add a filter. Even though there are people selling duct booster fans with filters, these type of fans are not strong enough to use with a filter and will be a waste of money. I have the cabinet divided into a vegging section and a flowering section. I am using a small bathroom type exhaust fan for the vegging space as it seems to be fine cooling that small space when using T5s.
A 4 x 4 tent will require a 6" centrifuge type fan--remember that it is 4 x as large as a 2 x 2.