Building a grow cab need help.

Hey im designing a grow cab and plan on using a pre-built cabinet and turning it into a grow cab. The space i have to work with will be around 2 feet deep by 32 inches wide by 6-7 feet tall and i already have purchased a carbon filter and fan which measure 8x8 inches by 20 inches for the filter and 9x12 inches for the inline fan which is 440 cfm but has a dimmer. My dilemma is which light should i get because i was hoping to buy a 400w cool tube however the shortest i can find is 24 inches long and with the ducting it seems that it will be too long to fit in the cabinet. Would i be able to run a 400watt light that isnt directly vented out or would it get too hot? Which lighting system should i buy i am hoping to grow 2-3 plants at a time. Would this light work www.amazon.com/Grow-Light-hydroponic-Pressure-Hydrofarm/dp/B005HKFZNA/ref=pd_sbs_lg_4

Click on the link in my signature to see my cabinet. A 400W definitely needs to be vented!