Why should one bother about the ultimate fate of the universe? One answer to this question is similar to the answer to the question about climbing Mount Everest: because the problem exists. It is in the nature of the human mind to seek incessantly new frontiers of knowledge to explore.
It is possible that those strange sentient beings of the far-future cold universe will find contemplating a warm universe such as ours not very pleasant, much as a nocturnal creature shuns daylight. But the more speculative amongst them may look back to our universe and to the Earth as an ideal world full of sunshine and a supply of adequate energy to last for billions of years, a dream world which will have passed away never to return. And what do we human beings do with this ideal dream world of ours? We oppress each other, build nuclear weapons for each other's destruction, and plunder the resources of the Earth!