Go to the rural Philippines and you'll find plenty of homes without air conditioning in 40+ heat.
You'll also find westerners accustomed to air-conditioning who live there and have "adjusted".
It takes about 2 weeks and your body makes some sort of adjustment.
It's an interesting phenomenon that maybe someone here can comment on more fully. By that I mean what exactly is happening to us when we adjust? Is it purely psychological or are there actual biological changes/effects at play? Whatever it is you really do "adjust" and it's not that bad after a few weeks. You even learn to sleep well at night in sweltering heat...again after you adjust.
Of course there are limits but we're built to handle the heat.