It’s all about load, temperature, and air density. Hotter air is less dense. Which means less oxygen for combustion (particularly important on non-turbocharged prop planes). It also means less “lift” under the wings. More load requires more horsepower and more lift. If a plane can’t show documented data that supports flying in those conditions, it is grounded by FAA rules.
Juan Browne, a pilot and part-time internet journalist who has been doing videos about the troubled Oroville dam in California, touched on this issue in his most recent video, towards the end.
https://www.youtube.com/watch?v=wDcCPGgwDgI
Just after the 11:00 mark in the video.