Lighting repeat question

I know it's been asked many times before, and I tried searching... biggest issue I'm running into is it's hard to get a straight answer when everything seems to be tailored to the specific person asking the question: SO anyways

I live in the desert so in order to keep the energy bill down, we set our AC at 81 degrees when inside that house and 85 degrees when no one is home... So basically, what I'm saying is it is not going to get under 81 degrees in my house. And since I plan on growing in a closet, it's probably going to be 85-90 degrees. I know this is hot, but it's not economical to cool the house down more. hah.

Anyways I was looking to grow 4 plants. Would a 250w HPS do the trick? Or do I really need to go the 400 watt? My grow space is pretty minimal. I'd prefer to keep it 1'2" w x 1'11" l x 5'6" h. But I might be able to tweak some to get it wider. The 1'11" however is set in stone, hah.

But in order to keep the heat down, would 250w HPS be able to still grow some nice plants with only four growing?

in lumens, the one I'm looking at is 33,000 lumens

 

Also, because of my heat issues, if I were to build a box, then I could build my own ventilation system, but it still wouldn't be a large ventilation system, would this be better?

Cuz I could probably do a 2'6"w 1'10"l 5'6"h box... but that's confining the heat even small, but could I then control the ventilation better? Kinda curious?

 

Thanks, though that wasn't quite what I was asking. I was stating the AC temps because that means even when I have a decent ventilation system, it's only going to be pulling air that, at BEST is 81 degrees. though more realistically would always be higher then 85 degrees. So I was just attempting to stress my heat issue and my need with a 250w hps as opposed to the more desirable 400w.

But ignoring the heating issues, would 250w hps be fine for four plants?