Do I have enough to cool my growbox?

Hi all,
I'm a lurker around here, done a few successful PC hydro grows, now im moving on up to the big boys with my 400W MH/HPS, I've got a guy building the box for me who is a food services industry major (knows what he is doing, had a beautiful NFT he made on display) who pretty much moonlights as a Hydroponic consultant to random people. My only concern is whether or not he knows what he's talking about as far as keeping the box cool inside, he claims that for a 400W box thats going to be about 24"x36"x~60" will only require only one GrowBright 4" Inline Fan & Carbon Filter Combo for outtake and just one 4" Inline Duct Fan that will cool the light and the rest of the box. I gave specific links so you could take a look at the fan speeds, etc. and tell me if this is gonna be enough to keep it cool? I'm just going to be using the cheap ass reflector that came with the entire light kit. Any help would be much appreciated. If I forgot anything please feel free to ask, the box is going to be in an A/C cooled environment usually in the low 70s (F).

The Analyst

pretty standard to use 4 inch fans i would rather use a 6 inch myself if growing in a small box or grow tent,
if the ducting is hooked up to a cool tube that will help a great deal
once you put a carbon filter on a 4 inch fan with a bit of ducting it reduces the extraction a fair amount from what is not that powerful to start with
a 6 inch turbo fan can move 3 times more air than a standard 4 inch fan

i have roughly the same space as you for my mother plants, i was using a 250w MH with a standard metal reflector
the temps were going upto 85f, the plants were fine as its veg, and high temps in veg are fine im using a standard 4 inch inline fan too for extraction
i dont think it would cope very well if i put a 400watt in there and flowered some plants, temps going upto 85f to 90 can increase the risk of problems

i would recommend
a 6 inch fan is not that much more expensive than a 4 inch one , its a good idea for sure
cool tubes are a great idea
maybe an active 4 inch intake too if you are set on only a 4 inch outtake
better to be safe than sorry, and you cant have too much fresh air lol better to over do it than under do it

peace

Get a 5" or 6" Inline fan around 250cfm and you will be fine. For the sake of saving 10-20 bucks you could have a lot of temp issues which would cause a whole load of problems. You can always turn the speed down with a controller if needed.

I would recommend getting that A/C unit for the summer months along with running your lights at night time