First off, WARNING. I've read a few reports of people being busted thanks to ebay/paypal.
Second, for a 400W, you definitely want the ballast to be remote. The heat from bulb and ballast will be intense.
I can tell you from personal experience, my closet is about 6.5'*3'. I was using 2*150W HPS and heat was an issue. I had to cut a hole in the ceiling for an extractor fan.