<...snip...> First thing I'd do is open the case and let the guitar adjust to the temperature of the venue. <...>
I do that with my guitar, flute, and saxophone. If the difference in temperature is severe, I'll do the same thing with my wind MIDI controller.
The last thing I do before we start is tune them up. My Parker guitar usually stays in tune the entire gig. The sax will need a slight touch if it's chilly, because my breath will warm the brass up a bit. The flute is the one that changes the most, but it's not difficult to retune.
<...snip...>Temperature will affect the tuning, and it doesn't affect all strings equally. Generally the heavier plain strings, and the wound strings with a heavier core, will go out of tune first.
I've noticed that.
I've also noticed a similar effect in the utility lines strung on poles. There is a lot more sag in the span between the poles in the summer, and they are more taut in the winter.
<...snip...>Temperature changes don't affect action much at all. <...>
I'm not a good enough guitar player to notice slight changes in action, it's my 7th instrument. Plus, I live in Florida, where the temperature never freezes.
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