Without a decent exhaust fan and passive intake, your temperatures will not only be too high, your plants will also lack oxygen. In addition, if you don't get a carbon filter, the smell will give you away in a couple of weeks.

My 400W HPS is a little over a foot away from my babies' tops. I have a 410m3/h exhaust plus passive intake. They are now 2 weeks old, plus 1 initial week of germination, and grow bushy without a heat problem. Nevertheless, I had to add another intake because it wasn't enough - with that, my temperature is now around 26 degrees celsius - ideal for my girls.

Imho, a 400W HPS is not suited for no-budget grows because it really heats up your cabinet. Either change lamps (someone else has an idea?) or spend some money...