Second attempt at growing

So I tried out growing some WW's a few months ago using LE and a homemade grow box. Unfortunately the outtake fans weren't strong enough, so I basicly burnt the plants and got worse than bush weed out of the grow.
Luckily I have more money this time, so I'm going for HPS and a better outtake fan. The space I'm using is higher as well.
The LE's will be used in a separate box for cuttlings and a mother and the new growspace will be used for 2 blooming plants at a time, or 4 if I'm experimenting with scrog. I will be growing in soil.

So here's what I'm going to add to my new space:
HPS kit 200W
Fan with carbon filter (I'm using a link since I don't know the English word for these kind of fans), 180/140 m³/h.

So my basic question is if this will be enough to clear and cool the air in my grow room. It's a closet with the following dimensions:
Depth: 50 cm
Width: 50 cm
Length: 150 cm

I'm also wondering if you think I'd be able to upgrade to a 400W HPS in this space, using the fan mentioned.

If I've forgotten to mention anything of importance, please let me know and I'll update the post. :)
Thank you in advance!