My sinew backed osage bow was "theoretically" a slug in warm weather, so I ran a few tests years back when I first bought a chronograph.
To test, I left the bow overnight in the vehicle when overnight lows were around 20 degreef F. I shot a couple strings of arrows thru it and found that around the 10th arrow I was getting a slightly slower arrow, about 5 fps slower. Several weeks later, I am shooting the same bow that has been kept warm in the house at 70 degrees. Virtually the same speeds, with very minor variation that could easily enough be attributed to sloppy releases. But the bow began to lose those few fps sooner...like the 5th shot!
I repeated the experiment several times at different temps but dropped the whole thing and threw out the records when I realized I was not getting any significant variation. YOUR MILEAGE MAY VARY.
Take all this with a grain of salt because it was late winter and humidity levels were almost zero here in the west during the whole time I was running the tests. If I pull out that bow today after a month of heat and humidity, I gar-ann-tee it will be like shooting pool with a well worn old rope.
And then there was the guy that told me that I needed to shoot only left feather fletching in the Northern Hemisphere because of the Coriolis Effect, right fletches in the Southern Hemi. Hehe, yeah, and I always remember to correct for the rotation of the Earth and lead my targets!