ventilation and heat question

my grow area is going to be 2 by 2.5 by 6 (about 30 square feet) completely enclosed.

Ill have a 400 HPS in there, but it doesnt have a cooled hood or anything. and gets damn hot

Ill have passive intake of relatively cool air (coming from attic) and 70 cfm for blowing air out of the box. The ventilation system should replace the air in the box about twice per minute.......right?

My question is if this ventilation of air alone will be enough to keep temps down in the box under 90F, or will i need to build some type of air cooled hood for my bulb? thanxxx