It's never really been clear to me what the "heat index" means.
Today in Philadelphia, at 4 pm, it's supposed to hit 95 degrees with 34% humidity; that corresponds, according to weather.com, to a heat index of 98. Tomorrow we expect 95 degrees and 43% relative humidity, for a heat index of 102.
What I've noticed is that the heat index here is almost always higher than the actual temperature. It'll get up to 95 on Tuesday, and someone will say "it `feels like' 102 degrees". No! It feels like 95. This is what 95 feels like around here. Sure, it might feel hotter than 95 degrees in the desert, but I've never been to the desert.
There are various formulas for the heat index. I suspect the second of the three given at Wikipedia is the "most accurate" in some sense, because it involves exponentiation of the reciprocal temperature, which is something which arises often in statistical mechanics; the other two are probably just polynomial approximations of it, which are easier to calculate, but ease of calculation is not so important. The various sources online seem a bit vague, though.
The following document from the National Weather Service states that the third approximation given at Wikipedia is, indeed, a polynomial approximation of the "true" heat index, which apparently depends on a fairly complicated biological model. In the end it probably just makes sense to resort to tables.
What surprises me is that none of the online formulas take into account wind. (The NWS document says that the wind is assumed to be a constant 5 knots in the model.) This seems silly to me. When I'm inside I can turn on a fan and be cooler than I would if the fan weren't on, because the fan dissipates the hot air around my body; shouldn't the same be true outside? (Michael Bluejay taught me this about fans.)
I think that the heat index is misleading, because it makes people think it's hotter than it actually is. I'd actually support replacing it with a number with an arbitrary scale, say zero to ten. If someone told me that tomorrow's going to be a nine on that scale, I'd know I don't want to go outside.
Also, weather.com has two forecasts that I look at regularly -- their ten-day forecast and their hour-by-hour forecast. The ten-day forecast says the high will be 97 today and tomorrow; the hourly forecast only goes up to 95. I suspect the reason is that at any given hour the expected temperature is indeed 95 degrees and the exact time that it will reach 97 is not known. Similarly, the forecast low Tuesday morning according to the ten-day forecast is 77, and the hourly only gets down to 78; the forecast low Wednesday morning is 76 but the hourly only gets down to 77.