Some thoughts:
Why is there a humidity problem in the attic, at least of a sort that can be corrected by pulling in outside air? Starting with the premise of the attic being full of air that came in from outside and has the same %RH, the attic warms it up. When you warm air you increase its moisture holding capacity so the same air with the same moisture in it will now have a
*reduced* %RH. So if there is a humidity problem it can only be because of some source such as a bathroom fan discharging into the attic. I'd correct whatever the issue is rather than using the fan to fix it.
I suspect you don't have a humidity issue and this is simply a feature of the fan. In that case set the humidistat to the high end so it never switches the fan on on account of humidity. If a separate unit then disconnect it.
As for temperature, oh I don't know. Maybe 120°? Or maybe so high that it only comes on when the air conditioning needs every bit of help it can get. If your AC system is good that could well mean you don't want the fan coming on at all! Think about it. How much does that fan draw, let's say
500W (maybe a tad high but go with it). How much does the AC draw (both inside fan and outside condensor)? Let's say 5000W. Ten times as much. That means 10 hours of fan pays for an hour of AC. I don't know how much heat load you get from a hot attic presuming decent insulation in the ceiling but my gut reaction is to say I'd rather put the electricity towards an hour of real air conditioning than 10 hrs of somewhat reduced attic temperature.
It's different of course if you have stuff stored up there that needs protection from overheating.
Be careful with fans that don't have ball bearings unless you are diligent about lubrication. Fans can seize up and then you are at the mercy of the overheat protection inside the motor. You might want to do a search for discussions of fires caused by attic fans.
Disclaimer: Non professional opinion only. Use at own risk.