Need some help with ventilation

Hello RIU

I am going to need a way to vent out the hot air and odor out of the room, and my budget is not in the range for a carbon filter and a fan. The room is in my basement, and it's dimensions are:
4 1/2 feet wide
6 feet deep
Almost 7 feet tall

I was thinking about building a box that is(in inches):
14" wide
16" tall
8" long

I would have a hole cut in my wall where the box would be placed, as well as a hole cut into the side of the box that would be mounted on the wall.

The box would contain carbon towards the top, where the ventilation hole is, so rising heat would pass through the carbon and loose it's smell.

Now I would placed a small powerful fan(one that can be bought at Wal-Mart or something) in the grow room on a shelf, so it would be pointed at and level with the hole that leads into the carbon box, would this work?
I could also place a fan ontop of the carbon box so it would help pull the hot air out of the box.

The air will disperse throughout my basement.

Would this idea work? Or would I need a more powerful fan?

Forgot to mention, I will be using a 400W HPS/MH light in the room.

Any help will be appreciated!

Not sure if I can post links
But for 140` you can get a fan/carbon filter combo
and its worth the money

I've seen links posted here before, so it shouldn't be a problem.