Air cooling three hoods

So, I'm going to be running 3 600 watt air cooled hoods. They will be hung in a line and connected with ducting venting out a window. I'm going to be pulling air through them from the adjoining room which is air conditioned. My grow room is a sealed room and insulated very well. My question is, will this air movement be sufficient to keep the heat down from the lights? Or with it being pulled through 3 lights, will it defeat the purpose? Thanks in advance.

depends on the fan's cfm and the incoming air temperature

Lets just say for an example the adjoining room's temp is 70, now how would I determine how many cfm's my fan would need to be. By the way, the total distance for the ducting coming in the room is 7ft, and this distance it will travel total, through the hoods and out the window will be about 25 ft. Also, my hoods have 6in. ducts.

Fan sizing CFM = (stands for) cubic feet per min = cubic feet of space you are exhausting, so take your sq ft of your room and height of room and calculate your cubic ft and there is your answer for the size fan( CFM) you need to move the air in your particular space in 1 min time

I know how to calculate cfm for a given space. I'm only cooling the hoods though.

Use a 6" inline fan to pull air through them and it will be plenty enough. I used an 8" inline fan (750cfm) with 4 1k watt air hoods in the middle of summer and it kept them relatively cool.

Did you run it continuously with your light schedule? Or did you cycle it on and off? What was your temp difference from running compared to not running?

Are the hoods on a closed loop, not removing air from the grow space, just the adjoining room? Or are you using that fan to vent the room also? If it is sealed what are you running for ac and co2 in the grow room?

Correct. The fan will be pulling air from the adjoining room through the hoods and out the window. I have a seperate fan with carbon filter to control smells. Would it do anything for temps if I ditched the second fan for hoods only and hooked them up to my carbon filter and pulled the grow room air through the filter, through the hoods, then out the window? Would pulling humid air through them be dangerous?