Hmmm... Is this a recirculating fan? How is your intake and exhaust set up? Do you have openings in the top of the space where heat is escaping? Could help to put a drop leg on your outlets if possible to trap heat when exhaust fans are off, but more info needed
The fan pulls air through my carbon filter from the top of box it pulls air in from the bottom through vents .lights on 77 degrees lights out with fan on 58 degrees
Turn off the exhaust. Your plants don't respire during lights out so airflow is only needed to prevent mold or bud rot. Keep a standard room fan running and you'll be fine. One thing the low temps will do is give some colorful buds...so you may want those cool night time temps.
The air that blows outside (outdoors?) is replaced by air from where? I've got a small wooden box I use as a mom cabinet. Two 40 w CFLs and two 4" computer fans run 24/7. One evening, I unplugged the power cord, and forgot to plug it back in. The plants were in a sealed box until I noticed the next morning. There was water dripping off the CFLs and the plants were sopping wet.
I would turn it off it you dont need it at those hrs for heat removal. Plenty off fresh air getting in other wise (right?) then you dont need it on unless it is part of odor control. Odor control is only reason i keep mine on in dark, but I dont have to worry about mold either.
I would get a second fan, use one to cool the light and circulate air within the grow space - drawing air from the bottom of the grow space and discharging toward the bottom of the space in a way that will create a natural circular airflow, and use the other to carbon scrub and exhaust - drawing from the top of the space in the most stagnant corner. Otherwise, just turn it off as mentioned Stoney baloney
I had the same issue in a small closet that’s inside my garage. What I did was buy two thermostatically controlled outlets one runs a 125w panel heater and the other controls the exhaust fan. The heater will come on when need (mine is set 67 def) and shut off before the fan kicks in at 78 deg. All can be found on amazon.
Once you get a feel for how the two stats interact with eachother you’ll be able to dial them in so that the exhaust fan/ scrubber will come on every so often. Might help with the smell a little. Sooner or later though you’ll need to let the scrubber run 24/7 to control the odor.
