How certain is the heat death of the universe? According to our current scientific knowledge, how certain is it that heat death shall be the ultimate fate of our universe, and why? Are there any serious hypotheses competing with heat death, and if such hypotheses exist, what are they based on?
 A: 
According to our current scientific knowledge

we know that we don't know what the 70% of the energy of the Universe is. Also, a comprehensive description of the thermodynamics of the Universe is impossible with the current standard Cosmological model and Einstein's General Relativity. In particular it's very complicated, and incomplete, as I said, to talk about what is now the energy of the Universe. Hence, its thermodynamical evolution has very low sense, with the current knowledge. It's only a speculative subject.
For a more satisfactory answer, I can give you  a brief naive explanation of why one can't talk about the energy of an evolving Universe. As you know and as we currently believe, we live in an expanding Universe. This is not a steady state, there is a precise time-line and a temporal asymmetry in its evolution, hence you can't define a globally a well defined conserved charge called energy, in the sense of the Noether's theorem. You can define energy only locally, according to the equivalence principle. Also, there is another problem called quantum vacuum whose energy is non-null and may even increase with the expansion of the Universe.
