When the human body gets too warm, it puts into effect all sorts of measures to cool itself down. Your skin secretes sweat for evaporation; at night, you sleep with your arms and legs spread apart to increase the surface area of the body; and all sorts of other things. In my case, it starts to happen in the upper twenties centigrade, i.e. in the eighties Fahrenheit, even though it may be a bit more or less for other people.
Still, this threshold when I start feeling hot is still noticeably below body temperature, which is roughly 37 °C / 99 °F, and I would think it is the same for most people. Why is this the case? You would think that as long as the outside temperature is below body temperature (which it is for most of the inhabited world pretty much all of the time), the body would still be busy heating, rather than cooling; as temperatures rise, the body would have less heating work to do, but it would still need to heat, not cool.