Few finalizing questions

I got my grow room up today and now its time to figure out what lighting and air flow I'm going to use now that I have my exact dimensions to working with. My grow room is in a closet that i build a wooden frame in and used panda film to create my own tent if you will. The dimensions are 3' 8"x2'x5' 3".

Now for lighting i would really like to use a 400w hps with a cooltube. I'll have my ducting setup like this:

outside->ducting->cooltube->ducting->outside

If i use a 6" duct fan with this setup will it cool the lamp enough to control temp in an area that small?

Now for exhaust would a 4" duct fan with a 4" carbon filter be enough for a room that small? Is bigger always better? I can always use a 6" duct fan with a 6" carbon filter, price is not an issue.

This room is going to be used for 2 possibly 3 plants in a DWC system each in there own container. If you guys need more info just let me know.