Unstable idle in hot weather

Hello V8 driver, who has ever been confronted with the following phenomenon:
==References====External links== 20 degrees and higher my V8 3.6 automatic has the following problem
in the empty leuf with pressed brake switching stage D the speed falls into the cellar, the engine goes out. When starting I have to leave the key turned because it starts but the speed goes back into the basement, engine out. When the key is held, the speed goes up again and then it runs. Who has an idea what that could be?