This question is basically the plot for this super famous and very thought-provoking sci-fi short story... Isaac Asimov - The Last Question. Here is the full text (only 9 pages):

https://physics.princeton.edu/ph115/LQ.pdf

This is one of those things I read a long time ago and it's stuck in my head because it is so profound. It really captures the battle of entropy vs negentropy (disorder vs order) at the end of the universe, and asks in a deep way if intelligence can ever truly understand itself or the universe that contains it.