I struggled with heat problems for years and in a closet it can be especially hard. Dont bother with duct fans, they don't have the power as Texas said. Your only options are:

1/ Cut hole into closet ceiling and vent to an attic or the like
2/ Ditch the closet and go with a C13 style cabinet (compact w/ excellent results esp. 400)
3/ Tex's advice (best option) about venting w/ a cooltube outside the closet

It all comes down to the fact that growing requires a good light (which you have) and a good inline fan like a Vortex or Squirrel Cage (which you can get), It took me 5 years to realize this but now my results are good and I am confident that a decent fan is money well spent!
BacchusGodofWine Reviewed by BacchusGodofWine on . Temp probs in my first closet!!!! Ok i built a grow area inside of my bedroom closet. the area was constructed of drywall and is approx. 5' tall x 4' wide' x 2' deep. i really dont have too much vent. and air flow for my one lovely lady and her hot 400w HPS sunshine except for a small 6" desk fan screwed into the inside of the cabinet and pointed up. My closet gets extremely hot inside if i close the little homemade door at the bottom. But then if i leave it open my room is extremely hot and bright and u can see it from Rating: 5