Ayatollah So
the spoof'll set you free
As you can see from the post above (by our mutual friend Ayatollah So) I'm disqualifed from answering that question. Have no fear however, I'm quite certain that our friend will explain it all for you.
A "heat death of the universe" is not guaranteed - here's a link with some interesting possibilities. Follow the link in there to "Dyson's eternal intelligence hypothesis." There are other hypotheses too. Bottom line is - too early to say what the long-run fate of the universe is.
As for the early universe, this link says
The early universe was nearly homogeneous, i.e. the same in different places. Our most direct measure of this uniformity comes from observing the microwave background radiation that was emitted when the universe was roughly 300,000 years old. The intensity of this radiation is a direct measure of how dense the universe was at that time. Looking at this background radiation coming to us from different directions shows that the largest density differences from one point to another were about one part in 100,000.
Thanks to gravity, this initially near-homogeneous distribution of thermal energy resulted in the wonderfully non-homogeneous distribution we enjoy today.