Effy,
You are correct, but perhaps overthinking this.
Indeed, with change in temperature, tire pressure changes (very little change with change in elevation).
SO, here is my recommendation:
Best-- weigh individual wheel positions and use heavier wheel position on each axle to go to your tire manufacturer's inflation chart. If only axle weights, see *1.
The chart will tell you the MINIMUM PSI for your given weight. Add 5 PSI to that minimum for a small safety margin.
*1 If only axle weights, you must add a fudge factor for side to side imbalance (say 5 PSI) as well as the 5 PSI for a small safety margin (as long as this does not exceed the wheel or tire limits).
And, yes, if you experience a 60 degree temperature swing, you WILL have to adjust tire pressure!
Remember when the tire manufacturers say PSI cold, they mean before driving at current ambient temperature.