+1 to pyrotechnic, this is it exactly.
as an example --
850.0 hPa, 10°C and 979.3 hPa, 30°C
have the same air density, 1.125 kg/m3
but don't have exactly the same trajectory, because, as pyrotechnic has rightly pointed out, the speed of sound is not the same
If using air density, practical error is usually not very big (something like ~0.3 mrad at 1km for a .308 class cartridge), but if an error can be avoided...
Also, unless using temperature-stable powders, the value of T is required for V0 anyway (because, if ignored, the effect is much more significant than 3 clicks at 1km).