250w temps

hi, i am looking to do my first grow in a 30" wide by 20" deep by 72" tall wardrobe, with a air system like this:
carbon filter --> 164 cfm fan --> air cooled hood with 250w hps --> exhaust
my question is do you think this would work and not be too hot, i plan on doing a scrog so i can manage the height of the plant, oh and there are 4 90 degree bends in the ducting, thanks.

I think that should work fine I am currently in the test/ construction phase with a similar box. I'm using a 270cfm fan to vent my 400 watt cool tube as well as another small fan inside the cab to circulate air. I vent out of the top of my box and I'm getting about 78f most of the day with an ambient temp of about 80 in the house. My box is currently just plywood but I will be insulating it this weekend with 1.5" rigid insulation foam. The best advice i could give you is to focus on sealing your light fixture really well and try removing the heat directly from your light. the box will still need some air flow too but it will be much easier keeping temp in your cab when the thing producing the heat is staying cool itself also you can get a fitting with a back- flow diverter to duct it all out of the same vent