、。。
For the record, this room doesn't have any AC or anything. All we've got is a paper fan.
Literal
Incidentally, this room [in-には] air-conditioning-equipment [thing-like-なんて] thing [topic-は] nothing not-exist. Exist-[thing-は] paper-fan [only-だけ].
なんて物 is the dismissive なんて + 物 'such a thing as X / anything like X' — often used when rejecting an exaggerated expectation. 冷房設備 'air-conditioning equipment' is a formal compound for what's usually called just エアコン. あるのはうちわだけ 'what there is, is only a hand fan' is a neat inversion using のは 'the thing that is' + だけ for a punchy 'only X is what we've got' pattern. うちわ (paper hand fan) is a cultural object associated with summer heat coping.