np man this is what i do ......helping other fix their troubles has made me near master lvl just need to work on genetics to claim that title
ok hot air .......think back in history class hot air balloons ......it will raise up .....ideally u want to have the carbon filter hanging in the upper part above the light hood itself
now u said a 4x8 i am thinking that looks like a basement so 7 foot ceiling to floor
4x8x7 is the area u have to control for grow ......224 cubic feet of air in that area
a 6 inch inline fan will do about 400 cfm(cubic feet a min)........about 370 with a carbon filter so that would be cycling the air out of your area nearly once every 42 sec(rough math in head)
carbon filter and inline fans should be matched to get the full life out of the carbon (to strong or to little the air will use up spots or all the carbon allowing smell to leak out)
http://www.ebay.com/itm/HYDROPONIC-CARBON-FILTER-6-X-18-ELIMINATES-ODORS-REFILLABLE-/161153827171?hash=item2585844163:g:tzAAAOxy4t1Sijq4
that is a refillable one........it matches close enough to be right for how it works on a 400cfm fan and the bends and all maybe 10 cfms over but will not hurt life........but after 12/15 months u just need to replace the active carbon in the filter to make it work again saving u 50 bucks on a metal work)
now if u really want to make any cooling be effective u should looking into insulted flexie ducting (it will not allow the heat to transfer back into the air as u are dumping it out)
ok u asked about a passive intake system and a active one
passive system is the simplest of the 2 as it is just a opening to allow the air to flow in ........the rule is simple u have a 6 inch ducting u need to double that and have a 12x12 inch hole to let in the air (just that simple)
active system system is the reverse of the exhaust system ........this method does allow cooler temps and keeps the walls of a tent from turning into a modern art project (with negative pressure u need stiff wall other wise suck in.....so the passive needs to be large enough to stop that or u add in a system to feed in air as fast as it is going out )......active but this needs a filter box (as u are going to completely change the air currents in your house u want the air going in to be clear of mold/fungi spores that have layered up over the drafty parts of the house ) ........the passive system allows most to settle back down before getting to area but a active system u are drawling them out a faster pace
as for conditioning the air .........with a exchange system like this u can not do it in the standard way (putting the gear in the area to control only that area).......u have to condition the air before it gets to the area ......the air that is getting sucked into the area has to be the way u want it as for it being in area the exchange is going to fast for the gear to really have any time to do anything to it
before u say i can slow down the air and give it time to work ........bad idea u have a fast moving system in a low part of the house .......this will make Co2 pool up around the plants (Co2 is a heavy gas...think oil and water with Co2 being water and Oxygen being oil) .........the standard rule is to have air exchange once every 3-5 mins for good healty plants .......i am a clear believer in overkill factor u can adjust what i have told u back down to standard rates.........but this will help controll the heat most effectivly