If I may be so bold, Elders, correct if I'm wrong.....

Your problem is more your reflector than your fan. It's like a toaster oven in there. If you get an air cooled glass sealed reflector and put your exhaust across the bulb after it goes out you'll be golden. Something like a cool tube or this:
Sunleaves Aurora 6 Reflector - Reflectors - Cheap Hydroponics - Indoor Gardening and Hydroponic Supplies - (Powered by CubeCart)
Doc Oc