Yes, things are closer together, but it’s a tiny effect. The electromagnetic force is many, many times stronger than gravity. Think of it like trying to compress a block of steel by standing on it.
For example, the density of the water at the surface under 1 atmosphere of pressure would be about 1000 kg per cubic meter, while in the Marianas Trench (about 1100 times the pressure), the volume would only be about 5% lower (about 1050 kg per cubic meter), a very small change for a very large increase in pressure. This isn’t nearly enough to generate significant heat, especially when it’s easily conducted into the atmosphere (which is wickedly cold in many places).
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