Yes it will, just like for example the Moon and Mars once had liquid cores that now have cooled down.
Funny fact. The core of the Earth would have long cooled down if it hadn't been for radioactive decay of various elements in Earth's core:
"For all this, however, Marone says, the vast majority of the heat in Earth's interior—up to 90 percent—is fueled by the decaying of radioactive isotopes like Potassium 40, Uranium 238, 235, and Thorium 232 contained within the mantle. These isotopes radiate heat as they shed excess energy and move toward stability. "The amount of heat caused by this radiation is almost the same as the total heat measured emanating from the Earth."
Funny fact. The core of the Earth would have long cooled down if it hadn't been for radioactive decay of various elements in Earth's core:
"For all this, however, Marone says, the vast majority of the heat in Earth's interior—up to 90 percent—is fueled by the decaying of radioactive isotopes like Potassium 40, Uranium 238, 235, and Thorium 232 contained within the mantle. These isotopes radiate heat as they shed excess energy and move toward stability. "The amount of heat caused by this radiation is almost the same as the total heat measured emanating from the Earth."
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The temperature at the Earth's core is estimated to be somewhere around 7,800K, or roughly the same as the surface of the Sun. The cooling of the core is estimated to be at about the rate of 100degrees C per billion years. The Earth probably has about 5 to 6 billion years left before the Sun swells to become a red giant and swallows it up. So the short answer to your question is yes, but by a comparatively small amount.
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Not before the sun blows earth up. It has radioactive isotopes decaying that keep its heat as well.
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Yes, 2 billion years in fact. Though the earth will be too hot for life in 1 billion years anyway.
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No,but it will eventually be vaporized by the sun.
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When hell freezes over.
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sure, why not