I think people make way, way too much of this. The entire point is that a tire (with a given load on it) has a minimum inflation pressure ... whatever the conditions you simply do not want that pressure to drop below that minimum (I am ignoring the upper pressure limit here). The entire assumption behind "cold tire pressure" is the assumption
that as you drive the tire pressure will go up from there (due to temperature rise from friction - generally
a good assumption). Ambient conditions (mostly local temperature) will affect that validity of assumption. Living in MN have driven from very cold conditions into warm conditions in a single day. One day driving south starting at ~0 degrees I drove into warm conditions that caused an over-pressure conditions in the tires at about 3pm .... even though in the early morning (cold temps) the tire pressures were just fine. The converse has also happened (and here is where I think your answer really comes out
): starting the morning in southern Missouri my tire pressures were just fine (5 psi over minimum in fact). Driving north into MN the temperatures dropped to zero degrees. Towards the end of the afternoon, even though I was driving at 60 mph or so, the tire pressures dropped to bare minimum (I barely avoided having to get out and run my compressor at those temperatures). If I had not had that 5 psi overage to start with ... I would have been 5 psi or so under
minimum at the end of the day.
These are extreme temperature swings that most of us do not see ... but hopefully it serves the purpose of example. The essence of the point is that for your ambient temperature
you want to avoid the tire pressures falling below your minimum, and that the temperature (and thus the pressures in the tires) is typically lowest in the morning (and before you start running the tire). Lower the tire pressures to that minimum when they are hot from running, and you risk a below-minimum pressure when you start the next morning when the tires are even colder. I do not believe making that adjustment when they are warm is any problem at all as long as you check and correct the pressures if/when they cool off (i.e. if you stop for an extended break, or overnight).
(more nerdy answer follows. FWIW (and it wont matter to many of you), I have a doctorate in chemical engineering (so this stuff is right up my wheelhouse - as it would be for especially for a mechanical engineer, and to an extent for may of the sciences). Two things will affect the tire pressure: temperature and local pressure (i.e. altitude). The easiest expression of pressure versus temperature is the "ideal gas law", which simplifying in this case would be (Pressure = [constant]*Temperature). Temperature goes up (either due to friction or rise in local temperaure) and the pressure goes up. Altitude (i.e. local pressure) ... this is way mis-understood. I regret contradicting Ployian, whom I quote at the start of this, but because local pressure goes down as you go up in altitude, the difference
in pressure between the inside of the tire and the outside goes up an amount equal
to the reduction in atmospheric pressure (this is stated in the linked article if you read it through to the end). But this pressure change for all but the most extreme altitudes is only a couple psi. The effect of temperature is MUCH more significant. We maybe get confused because as you go up in altitude it just gets much colder at night (which makes for lower tire pressures in the morning - but this is just because of the lower temperature, not the altitude per-se. Bottom line: temperature is much more significant that altitude - so ignore altitude and pay attention to local temperature to flag changes in morning tire pressures.
At this risk of making this way too long ... a specific example: on my recent run from Fresno CA to Minneapolis (via Reno, Salt Lake, southern Wyoming, Nebraska, etc: started out in Fresno at 65F with morning tire pressures set at 90psi (85 psi is my minimum). Reno and Salt Lake with altitude maybe 3000-4000 feet and morning temps around 60 my morning tire pressures were around 86 (ok to go). Laramie Wyoming, at 8000 feet (where you would expect raised pressures from altitude alone), but
morning temperatures of 48 or so, gave me tire pressures of 80 psi (5 psi below my minimum). I did not correct pressures, but waited for air temperature to rise enough to give me my minimum of 85psi). The next morning, in Nebraska back down to ~2000 feet, morning temps were about 65, and my morning tire pressures were back to 87 or so. (I did not
add or remove air to my tires during the entire 5600 mile trip).
Anyway ... this is way too long - hopefully for those who wade through it it helps