Dew point and relative humidity, along with temperature and wind, are crucial measures to predicting how you will feel.
https://en.wikipedia.org/wiki/Dew_point
https://en.wikipedia.org/wiki/Humidity#Relative_humidity
In the US, the 100th meridian is a popular demarcation for the half of the country that experiences high humidity versus the other half that experiences low humidity. It is why 100F in Phoenix, Arizona is much more tolerable than 100F in Atlanta, Georgia.
Do any feel-like estimates take cloud cover into consideration? It doesn't seem like it, but in a high altitude desert like NM, it is a huge factor. Furthermore, the magnitude of the effect varies depending on the day of year and time of day (how much atmosphere the sun passes through), so you can't just mentally add 10 degrees or something. And it isn't just based on the immediate conditions - if it has been cloudy all morning it will feel cooler even after the sun comes out then it will if the ground has been baking in the sun all morning. Some of that is accounted for by the air temperature (conductive heating of the air by the ground), but there is also a radiative heating effect as well. I would love an app that tried to incorporate those factors into it's "feels-like" estimate.