Are you exhausting through a carbon filter?
The cfm of a fan is only part of the story. Usually this rating is measured by running the fan in open air with very little resistance or back pressure. The other spec is 'static pressure' which is a related to how much pressure a fan can deliver to overcome back pressure from a constriction like a filter. It's like the difference between, say, flapping a blanket which moves a lot of air at low pressure or a bicycle pump which delivers much less air but at much higher pressure.
Personaly I doubt a window fan will move much air through a carbon filter. OTH your grow space is small and it may be enough.
If you have a use for the fan anyway, even if it doesn't work, why not try it. Otherwise I suggest a 4" or 6" inline duct fan
for example:
http://www.amazon.com/LED-Wholesalers-GYO2402-Hydroponic-Booster/dp/B003YFADW8/ref=sr_1_1?ie=UTF8&qid=1307289712&sr=8-1