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This may sound like a dumb question to any geophysicists out there, but if the temperature at the center of the Earth is so darned hot, why isn’t it the same for Mars - or the moon?

Not dumb. No question is. But first on the Earth.

'We' have a molten heavy metal core, it gives off heat and our magnetic North and South poles, so Iron must be 'down there', along with Uranium. But without that molten Iron we'd be screwed as the Sun's and other Space Rays like X and Gamma would fry us (Gamma Rays are the Big Killer Gun in the Universe). The Aurora Borealis are atomic particles ('the Solar wind') being drawn to our magnetic poles. Magnetic North is never at our 'North Pole' and varies from location to location. It's called 'Declination' and where I'm at it's -3.2^o (very important to know 'in the field').

Now to the Moon and Mars, I'll take Moon first:

Moon: The moon was created when Earth V1.0 was hit by another proto-planet (can't recall its name now, so call it 'X') in our young solar system days. A part of planet X combined with Earth V1.0 (thank you Gravity) to make it today's size, Earth V2.0, but a huge chunk was thrown into space. Gravity took over and gave us the 'moon'. So it's solid rock, no molten core like Earth. And therefore no heat. That's why the Apollo Missions were somewhat of a bust. It's the same 'rock' Earth is made of, and same age. NASA was hoping for something else.
Oh and originally the moon's orbit was much, much closer to the Earth than today. And it's orbit keeps growing, 38 mm per year (sorry for the Canadian measurement), so one future day it will be 'gone', and that will have dire effects on the Earth - but we'll (Humans) be long dead.
Mars: Mars once had a liquid (molten) core like the Earth and with that, heat and an atmosphere, and also flowing water. But the core solidified, and Mars lost 'everything'. Also, without a molten core Mars has no real 'North' or 'South' so a regular 'army' magnetic compass wouldn't work there. 'The WHY' Mars' core solidified is still being studied (to my best knowledge). And without a magnetosphere Mars is always bombarded with those nasty killer Rays (atomic particles).

Hope this helps.
I wouldn't write a Thesis on the above, but it'll get you a passing Grade -- and impress Chicks at a Bar :-)

Thank you for a most informative and excellent response.

Another problem for Mars and us is that being somewhat smaller, the escape velocity from Mars is lower. Thus it has lost a lot of its atmosphere over time, and who knows what greenhouse warming potential. It will thus be very hard to live there if we do go. Recently read Ben Bova’s book on Mars. Anyone know how accurate it was in its descriptions?