It's to lower the temperature in the whole place.
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Waïti'Premises' is just another word for 'building'. Not sure but I would think mostly used in the US ?
Also it would refer to an office building or administrative building (or school like in your example).
For instance 'to enter the premises' or 'to leave the premises' are usual expressions. A little bit formal though I would think...
Waïti.