Probably won't need a cool-tube. I have one I don't use it, one 400w Hps seems pretty cool actually.
In a 'normal' medium sized room it would barely heat if ambient is under room temp avg, Bro.
Radiant should be pretty on the ideal 25+ Celsius, I find around ambient in tent is -5 that "ish". That's a tent 1.2m so 3 or more feet,
So you should be on the money with 250+ CFM vent, bro.
I use an Adjustawing Medium Avenger with a 400W bulb. It is okay for 4x3. Better for 3x3.
I don't think a 400W set up is going to give you enough lumens over 4x5.
The Adjustwing is probably one of the better reflectors too!
You'll be vegging for a long time in a one plant 4x5 scrog.
A smaller tent 2x3x3 or a bigger bulb (600W) would be my advice.
With the AdjustWing.