How necessary are cool tubes?

I have this 400W HPS from HTG Supply ( High Tech Garden Supply ). I am going to set up a Grow Box with this layout using CFLs in the mother and clone veg chambers and the 400W HPS and some CFLs for good measure in the flowering chamber. The ballast for that light will be sitting on top of the box and the light of course will be in the flowering chamber.

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I am planning on using passive intakes and active exhaust in all 3 of the chambers. 2 of these 6" duct fans will be used in the flowering chamber for ventilation: ( High Tech Garden Supply ) along with 2 good sized passive intakes in the chamber opposite wall from the exhaust fans. I will be using 4" PC fans for exhaust with passive intakes in both the mother and clone chambers.

With this setup, how necessary is setting up a cool tube for the light? Will the two 6" duct fans be enough to vent the flowering chamber without a cool tube? With the chamber being 6' tall, I would assume that should leave enough room for the plants to grow as tall as needed with room for the HPS to be far enough during growing?