Is geothermal energy exhaustible

Answer 1

I should think not.

The center of the earth heats up because of the large mass of the earth which creates the gravity. The gravity of the earth packs the particles very tightly together creating high pressures. When particles are under high pressure they vibrate more violently together which creates heat. Therefore until the universe explodes the earth's core should continue creating in-expendable amounts of heat.

Don't hold me to this answer - but it makes sense to me

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The Earth's internal heat is from natural radioactive decay of uranium and its active by-products, not from compression, as is the initial condition within a young star before nuclear fusion can start.

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Early geologists did think the Earth's internal heat was that left from its original accretion, and so tried to calculate the planet's age from its black-body radiation cooling curve - but soon realised this gave an answer far short of reality. Your hypothesis is roughly the same as that.

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As for the universe exploding... it may eventually shrink but the Sun will have died as a red giant and scorched the Earth to a cinder long by then.