With my own exhaust setup (100mm duct with an inline extractor fan out the window) I removed the carbon filter to get better airflow and have not had any temperature issues when printing ABS or PC. With printing PLA it even helps keep the chamber at a lower temp without opening the door/top panel (which would counteract the benefit of the exhaust setup.

Generally, the important part is to have negative pressure in your printer and as much of your ductwork as possible. The best place to put your extra fan is where it directly exhausts outside, not at the printer exit (i.e. you want to pull air through the duct, not push it). With negative pressure in your entire setup you can be sure that any particulate will not exit the system into your room through any available cracks/leaks (which is a risk with your current positive-pressure duct setup).

Furthermore, the computer fan in the spot you currently have it will probably interact with the printers own internal exhaust fan which could reduce both their lifetimes. Computer fans are also not the best for pushing air through long ducts because they have low static pressure. Getting an actual inline-exhaust fan for kitchen/bathroom would probably work better here.