What is above the closet? If it is an attic, you could simply run a duct through the ceiling and into the attic. Install a 4" inline fan on the end in the attic and let it exhaust there. I have (2) 4'x4' flowering areas stacked in a 5'x7' walk-in closet with (2) 1000W HPS lights. I run a perpetual grow that yields 16 plants for harvest every two weeks. Ventilation is handled by 6" ducts from each light that are tee'd together and fed into the attic. A six-inch inline fan is installed in the attic and I exhaust it facing my ballasts to keep them cooler
View attachment 2369762. I keep the room at 75F and the air pumped into the attic is right at 80F. Anyone walking into the spare bedroom sees, hears and smells nothing.