I must disagree.
Pressure deviation is exactly what affects how a bullet flies. More dense air= more resistance to the bullet=more drop.
Temperature alone has no bearing on how a bullet flies, other than how it might affect a temperature sensitive powder's burn rate and subsequent velocity deviation.
And elevation affects ballistics due to the pressure difference at changing altitudes. The higher you are, the lower the barometric pressure. But hotter or colder air alone will not affect bullet flight, only air pressure does!
Many ballistic apps calculate pressure by elevation, temp & rel. humidity. But if you had to rely on one unit of measure to base a ballistic chart from, it would be barometric pressure measured in real time.
Lots of shooters do this and it is very simple to apply. When inputting data into a ballistic app, set your ELEVATION TO "0". Then, read actual pressure from your shooting position with a Kestrel. Then enter that actual measured pressure as "station pressure" in the app. That way, the app does not need to "calculate"pressure, cuz you just gave it an accurate measured value from your shooting position...
If I were shooting long range at different elevations, I'd use proven data from an app at a measured atmospheric conditions as a baseline. Then, enter the real time station pressure at the time of the shot for the app to correct for the difference in pressure. Temp and elevation inputs won't matter if you have station pressure measured...
A second way to correct for pressure changes us to use Density Altitude. The higher end Kestrel units can calculate DA, and you can make a ballistic chart using DA to compensate for elevation (read pressure) changes during a high altitude hunt. Lots of good "how to" reading on DA and station pressure, if you are interested.
Good shooting...