Adding exhaust fan to upstairs loft?

[az1324]

I have a ~800 sqft 2nd floor condo unit with a small loft area (~100sqft, ~600 cuft) adjacent to a vaulted ceiling living room. The rest of the condo is 8ft ceilings with attic space above. There is central ac but no vents/intakes in the lofted area. Needless to say it gets hot up there. It is not a frequently used space at this time, but I was thinking of installing an exhaust fan at the top of the wall which would draw the air out a roof vent. Hopefully this would also draw in cooler air through the windows on the main level and cause a cooling effect in the whole space and reducing the need for AC use which is currently only a few times a year on very hot days.

The attic space is adjacent to another condo unit so I cannot install anything loud and I do not want to add any additional vents to the roof so I want to tap into one of the existing bathroom/kitchen exhaust vents.

The question is if I install a bathroom style exhaust fan with a there will it high enough cfm (100-200) to be effective?

Any other suggestions?

Thanks.