postoak,
Yes, I did the "warm weather" experiments with .416 Remington factory ammo.
Through a reader, I obtained a box of ammo from the early 1990's (the cartridge was announced in 1988, loaded with 400-grain Swift A-Frames. I waited for a 95-degree day in August, about as hot as it gets in this part of Montana. After shooting some of the ammo at 95 degrees, I "green-housed" three rounds in a clear Ziplock bag with a small thermometer, placing the bag on the bench in the open sun until the thermometer read 110 degrees. There was no discernible difference in velocity, and the average chronographed muzzle velocity 15 feet from the muzzle was 2459 fps.
There also weren't any signs of excessive pressure. The rifle was a Model 70 Classic with a 23" Lilja stainless barrel, and the bolt opened easily after each shot.
A couple months later I obtained a box of new Remington factory ammo, also with the 400-grain A-Frame, and shot it on a 50-degree day, typical of what might be expected in Africa on a cool morning during a buffalo hunt. I had some ammo left from the "old" box as well, so shot both for a comparison. The new ammo averaged 2392 fps and the old 2450 fps, so Remington may (or may not) have reduced the pressure a little from the early days of the round. Statistically 58 fps isn't that big a difference.
But the main point was that there wasn't any trouble encountered with the old ammo in hot weather. Now, it wasn't first-year production ammo, and my rifle may have had a somewhat smoother chamber than a typical factory rifle. But that's what happened.
