Does the exhaust fan vent directly to the outside, or does it vent into the attic near a screened opening?

It might be to your advantage to have a professional look at how the vent is installed. S/he might be able to make the exhaust system much more efficient.

Go to Houzz Professionals. Scroll down to HVAC and/or General Contractor. Click. Enter your zip code in the search box with the tiny magnifying glass. Look at the work of the professionals in your area. Contact one or more of them directly for a consultation.