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The sun is hottest at its core because of the pressure. When gravity pull the atoms of a sun together, it exert higher pressures at the core of the star than at the surface. The earth's sun is approximatley 24.5 millions deg F at the core but generally no hotter than 10,000 deg F at the surface. However, surrounding the sun is an outer atmosphere called the corona. If you have ever seen a picture of a solar eclipse, the corona is visible light beyond the shadow cast by the earth. The temperatures of the corona varies greatly, and the hottest spots have been estimated at around 36 millions deg F, e.g. hotter than the core. So for this reason, you can say that in spots, the sun's surface is sometimes hotter than its core.

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