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On earth, using earth-sheltering techniques can significantly reduce the temperature fluctuations on a structure. Would the same statement be true as well on the Moon? Does the Moon's core still contain significant heat?

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On the earth-sheltering question, the answer is yes, using material to increase the thermal mass of structures would work just as well on the Moon as on Earth. There might be minor differences due to different materials and lack of water in Moon soils but the general principal would still apply.

As for the Moon's core still containing significant heat, that answer is no. At least not compared to the Earth. Smaller bodies cool much more rapidly than larger bodies as their surface area to volume ratio is much higher and therefore they can radiate heat faster. The Moon's core cooled off much, much faster than the Earth's and most of the latent heat of formation is now gone. There is probably still some heat left from decay of radioactive materials but it is much lower than what the Earth has.

An indicator of the lack of interior heat is that the Moon is very seismically quiet, there isn't much going on under the surface. Seismographs place by the Apollo missions showed very, very little activity. If there were heat and significant liquid portions to the Moon's interior, there would have been much more activity on the seismographs.

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The core of the Moon has solidified. This is evident from the fact that the Moon always show the same side to the Earth (except for a bit of wobbling). Consider eggs - hardboiled eggs are much easier to make rotate by spinning than raw eggs.

How much it has cooled below the melting point I do not know, and whether you consider this significant.

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Well, no, the Moon always show the same side to the Earth due to tidal locking; I am not sure if your intuitive explanation still applies. – zakk Jun 30 '12 at 15:52
Tidal locking only works well with solid bodies. – Thorbjørn Ravn Andersen Jun 30 '12 at 16:15

No, the moon formed when a small mars-sized planet crashed into the proto-earth. This was after the earth was almost fully formed so all the denser materials had sunk to the core and the outer ones "fell off" and became asteroids. These less dense asteroids flew off and were slowly pulled together to form the moon. Therefore all the hot parts of the earth had cooled by the time the moon formed. This means the core may still have some heat but not a significant amount.

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Sorry I didn't answer the other questions but it would reduce temperature fluctuations. – Cameron Jun 13 '11 at 15:04
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Instead of commenting on your answer, you should just edit it to include more info. – voithos Jun 13 '11 at 18:41
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But surely the Moon still had to undergo differentiation to become spherical? Wouldn't this give rise to frictional heating? – Daniel Blay Jun 30 '12 at 12:13

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