Well, what alternatives are there to using a Window AC unit, because a window ac unit would require me to cut thru the wall and mount it in the designated spot.

Is there any alternative?

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Say I did get a AC unit, cut out the slot, add support for it on the other side(making sure it wont fall thru). What would this take care of? Would this take care of my temperature control, and humidity? Would I still need to let in new/fresh air in the closet every so often?