If you're trying to run the attic cooler to stay more comfortable indoors an attic fan is about the worst way to go about it. Attic ventilation is not about cooling, and it's DEFINITELY not about mitigating radiated heat transfer from the roof deck directly to the insulation. (The breeze outdoors didn't exactly stop the sun from heating up your roof, did it?)
Like I stated before it takes a heluva lot of attic ventilation to have a relevant effect on cooling. Attic ventilation is about keeping it dry. Unless the ceiling is perfectly air-tight an attic exhaust fan even adds to the load of an air conditioning system, since it draws conditioned air out of the house by pulling it up into the attic first.
To address the cooling load issue head on:
If the insulation is fiberglass, it's somewhat translucent to the infra-red radiation, making the temperature an inch or two into the fiberglass layer hotter than the attic air, since it's absorbing the radiated heat from the even hotter roof deck. Overtopping it with even a couple inches of blown cellulose insulation stops the IR radiation at the surface of the insulation, which then runs at about the same temp as the attic air, not the temp of the roof deck. Cellulose is opaque to the radiated heat, so it heats up on the surface, not at some inner depth.
Painting the under side of the roof deck with a low-E "radiant barrier" paint, makes a difference. More expensive but also more effective, perforated aluminized polyester type radiant barrier applied to the underside of the rafters makes a bigger difference. If you do both, the attic air temperature will run cooler. Don't use aluminized mylar or bubble-pack versions, since those are vapor barriers, and can create a moisture problem where none existed previously. The perforated aluminized fabric type radiant barrier run about 5 perms, about as vapor permeable as standard latex paint, which is fine.
If you're due for re-shingling, a high solar reflective index shingle (SRI greater than 50) would also make a dent. If the pitch is 2:12 or lower an even higher SRI would be appropriate.