Heat death paradox

Formulated in 1862 by Lord Kelvin, Hermann von Helmholtz and William John Macquorn Rankine, the heat death paradox, also known as Clausius's paradox and thermodynamic paradox, is a "reductio ad absurdum" argument that uses thermodynamics to show the impossibility of an infinitely old universe.
This paradox is directed at the then-mainstream strand of belief in a classical view of a "sempiternal" universe whereby its matter is postulated as everlasting and having always been recognisably the universe. Clausius's paradox is one of paradigm. It was necessary to amend the fundamental cosmic ideas meaning change of the paradigm. The paradox was solved when the paradigm was changed.
The paradox was based upon the rigid mechanical point of view of the second law of thermodynamics postulated by Rudolf Clausius according to which heat can only be transferred from a warmer to a colder object. It notes: if the universe were eternal, as claimed classically, it should already be cold and isotropic (its objects the same temperature).
Any hot object transfers heat to its cooler surroundings, until everything is at the same temperature. For two objects at the same temperature as much heat flows from one body as flows from the other, and the net effect is no change. If the universe were infinitely old, there must have been enough time for the stars to cool and warm their surroundings. Everywhere should therefore be at the same temperature and there should either be no stars, or everything should be as hot as stars.
Since there are stars and colder objects the universe is not in thermal equilibrium so it cannot be infinitely old.
The paradox does not arise in Big Bang nor modern steady state cosmology. In the former the universe is too young to have reached equilibrium; in the latter including the more nuanced quasi-steady state theory sufficient hydrogen is posited to have been replenished or regenerated continuously to allow constant average density. Star population depletion and reduction in temperature is slowed by the formation or coalescing of great stars which between certain masses and certain temperatures form supernovae remnant nebulae - such reincarnation postpones the heat death as does expansion of the universe.