The temp swing with that A/C unit will be more than you want to control fermentation. You'll need a temp controller & set it at ~2F differential. That A/C unit will not work with a temp controller because it's digital/remote. You need an analog unit or be a real fancy electrician to bypass the electronics in the A/C unit. 7000BTU in an 8x8 box should be okay for a lager fermentation @~50F. If you're thinking about lagering in it I doubt it could handle it.