I once spent most of the summer in a WW2-era building with no AC in the southeastern US (Ft Benning). I imagine it is both hotter and more humid in much of India.

Short answer is that you get used to it. There was a surprisingly effective swamp cooler that worked about half the time (we got pretty good at troubleshooting it) and several ancient pedestal fans. You can sleep in very nearly any environment once you become sufficiently sleep-deprived.

Probably outside to catch the breeze. We lived i like a concrete bunker so it was good at holding in heat at night.