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There seem to be two separate questions here:
<blockquote>Would a moon colony need to be deep underground to get more gravity?</blockquote>
No. This is basic physics.
Going deeper into the a gravitational body reduces gravity. Think of the limiting case where you are in a hollow chamber in the middle of the moon. Gravity would pull equally in all directions, cancelling out. You would be weightless there.
<blockquote>Would a moon colony need to be deep underground to get more natural heat?</blockquote>
~~Huh? What does "natural" heat mean? What would be unnatural heat?~~
The answer is probably "no". The main source of heat on the moon is sunlight. Going deeper would reduce fluctuations to get closer to the average, not not really much more heat. The moon is too small to retain much fossil heat. The small volume relative to the surface area also means that heat from radioisotope decay is much less significant than on Earth.
A lunar colony would likely use solar collectors as a significant source of power, including heat. The main problem with that is the long nights, and therefore need for a large amount of storage, or additional power generation, like nuclear reactors.

There seem to be two separate questions here:
<blockquote>Would a moon colony need to be deep underground to get more gravity?</blockquote>
No.
Going deeper into the a gravitational body reduces gravity. Imagine an object in the very middle of the moon which doesn't get destroyed there; Gravity would pull equally in all directions, cancelling out, so that object won't be pulled anywhere.
<blockquote>Would a moon colony need to be deep underground to get more natural heat?</blockquote>
The answer is "no". The main source of heat on the moon is sunlight. Going deeper would reduce fluctuations to get closer to the average, not not really much more heat. The moon is too small to retain much fossil heat. The small volume relative to the surface area also means that heat from radioisotope decay is much less significant than on Earth.
A lunar colony would likely use solar collectors as a significant source of power, including heat. The main problem with that is the long nights, and therefore need for a large amount of storage, or additional power generation, like nuclear reactors.