I think the phrase 'HPS in rubbermaid growbox' translates in Ferengi to, 'Oh crap! Fire! Run!' Heh, just giving you some shit.
The *room* (containing the growbox) will increase in heat, unless you have air conditioning or a heat pump or a fan to move the heat out of the room. But I've lived with a 400-watt light *and* a 432-watt (low profile fluoro) in my room for years, and it's not significant. Actually, in the winter it probably saves a tad on heating (but takes a little extra air conditioning in the summer of course). A beefy computer probably emits more heat than a 400-watt HPS light.
Your fan seems too small though. I cool my 400-watt cooltubed light with a 440 CFM 6" fan that is dialed down to move around 200 CFM. (A 6" fan spinning slowly to move 200 CFM is quieter than a 4" fan roaring along at full speed.) 80 CFM, I dunno, that seems a little light. Doesn't hurt to try it though, as long as you don't let the heat build up and cook your plants. In fact, I'd try it first with no plants in it, just to be safe, and have a backup plan in mind if the 80 CFM isn't adequate.
Also, what kind of fan? Many kinds of fans will burn out their motors if they experience significant back pressure (e.g. if they have to suck against resistance). That's why most folks use centrifugal fans: they are designed to handle that stress.