Why is the center of the earth so hot

Why is the center of the earth so hot?

Is it cooling from the big bang?

A reaction?

It's amazing that he continents are "floating" on molten rock, yet the surface is cool. How would life on earth be different if the center of the earth was not hot?

Or is that impossible?

Is the center of the moon molten? Or is the moon too small for that?

The heat of the earth's center is primarily derived from heat left over from planetary accretion (that is, energy released when a whole bunch of debris was agglomerated into the earth under the force of gravity, the potential energy of the debris was transformed into heat energy and et cetera). But actually, the majority of the heat of the earth's core is theorized to come from the decay of radioactive elements (we can't know for sure since we can't directly study the earth's core).
If the center of the earth were not hot, life would not exist on earth, or would exist in an extremely different form. The movement of the molten outer core is theorized to be a major factor in the formation of earth's magnetic field, or magnetosphere. This magnetic field acts to protect the earth from the solar wind, which is a powerful stream of ionized particles ejected from the sun's own atmosphere.
The moon does in fact have a melted outer core and a solid inner core similar to the earth's. However, it's core is quite small relative to its size and does not generate an appreciable magnetic field.
On a tangent, an interesting theory about Mars is that it once had a much richer atmosphere than it currently does, but that it was mostly stripped away by the solar wind over time, possibly because it's magnetic field is rather weak compared to Earth's (and there are other theories concerning the reason why Mars' field is so weak).

It used to be thought that the earth was just still cooling. But more recently its been discovered that much of the heat at the center of the earth is caused by nuclear reactions (fission or fusion, I'm not sure). This led to a re-evaluation of the age of the earth, just as finding that the sun works not by hydrogen 'burning' and combining with oxygen but hydrogen -fusing- to become helium led to a re-evaluation of the age of the solar system.

Why is the center of the earth so hot?

==> Radioactive decay of marterials in the core keep it molten.

It's amazing that he continents are "floating" on molten rock, yet the surface is cool. How would life on earth be different if the center of the earth was not hot?

I'm not sure if it is possible, but let's hope it doesn't go cold so we can find out.

Is the center of the moon molten? Or is the moon too small for that?

==> Our moon is too small to have a molten core