With closed circuit venting, how hot is your grow room outtake?

Hey guys,

I'm doing a wardrobe grow but am limited by space. As such, I was wondering if it's alright to put my intake for my cooltube ventilation system by the normal outtake from the grow room (pushed out via a carbon filter)?

Will the air being pushed out be cool enough for some of it to be sucked back in to be used in the cooltube to vent the lamp?

Sorry this was quite hard to word, hope you get the picture!

Thanks a lot for any help

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