We need to maintain a core temp of 98 degrees. Why this is so is another discussion.
Usually our skin temperature is about 85 degrees.
When the temperature is 98 or above, we are under stress.
High humidity, high dew point, is a factor. When the dew point is 90 or higher, sweating doesn't work very well, since the lowest skin temperature we can achieve by sweating is the dew point.
The body can't shut down it's metabolism to stay cool, so the heat produced by the human body, about 60 to 100 watts of heat, has to be dissipated. Even if your pretty well adapted to a hot climate, there is still the need to dissipate the heat of metabolism.
In air-conditioning, not only is the temperature reduced but so is the dew point. So then when we sweat, we can easily make ourselves comfortable.