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That's not where natural geothermal energy is from. It's residual heat from planetary formation and some natural radioactivity.

This form of storage also unfortunately only yields heat (via heat pumps or directly), not electricity, as the temperature difference is much too low in comparison to meaningfully run any heat engine from it.

Great if you need to heat houses; not so great if you were hoping to store the solar energy for a rainy, or rather cloudy, day (or night).

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No, that is how natural geothermal energy works. Perhaps you mistakenly thought I was saying the heat comes from sunlight? I didn't. The heat comes from below (or, in some cases, from internal radioactive decay). And this delivery of heat from below (or from decay) is a slow process, taking a very long time, which is why geothermal resources have to be buried deeply (otherwise, that heat just leaks out and the temperature of the geothermal resource is too low).
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Yeah, "accumulate the heat over thousands of years" indeed sounds a bit misleading to me. The heat is largely already there (or is generated pretty uniformly through radioactive processes), it's just slowly transmitted outwards down a gradient.
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