Our universe is eternal, expanding indefinitely, and not threatened by any form of 'heath death'. All evidence points into this direction. In fact, at the end of the nineteenth century Ludwig Boltzmann had collected all the evidence to draw such conclusions. His consistent reasoning on how to render the reversible laws of physics compatible with the second law of thermodynamics brought him close, but he failed to make the final decisive steps.
Ok, I realize that at Boltzmann's time our knowledge of the universe didn't stretch beyond the Milky Way, the island of stars that we inhabit. And yes, I admit reasoning here with the benefit of a heap of hindsight. But even now, in the twenty-first century, this hindsight is apparently not distributed uniformly.