Do you remember how they were talking about pressure equalization or looking for other universes that existed at a lower pressure? It's a pretty direct mapping from the story to (neg)entropy; it's not related to climate change except in the very vaguest sense.
I disagree- these mechanical people are well-nigh immortal and will leave to see the end of their world, no one alive today on earth will live to see the heat death of the universe. However, we might just get to experience the effects of climate change.
The beauty of literature is we can both the right - our interpretations of the work is what matters. Additionally, while they are inspired by them,authors do not necessarily do a 1:1 mapping of real world issues to their stories