I ran a quick test and here's some data
. Measured the tuning of the guitar indoors (at 75F - the lower row). Put the guitar outside for about a half hour (in the shade) - where it was 10 degrees warmer ambient temp than inside. Didn't play the guitar, or move the trem - just moved it from inside to outside. So there's definitely a loss of many cents of tuning with increased temp/humidity (although it's not a humid day). I imagine the difference may grow if it was a wider temperature change.
Just as a recap, my issue is I'll acclimate the guitar at the venue for an hour+ prior to the gig, and have it tuned up to start the show. A few songs into the gig, I'll check the tuning and it will be flat be this much or more.
View attachment 123200