The inner core is solid , though it is hotter than the liquid outer core.
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The inner core is indeed hotter than the outer core. However, the PRESSURE on the inner core is greater than the pressure on the outer core and the melting point of iron, the main constituent of the core, INCREASES as the pressure goes up. So, because the pressure effect overrides the temperature effect, the inner core is solidified.
We also can speculate that the inner core began to freeze (solidify) about 1 or two billion years ago. the inner core makes up only 1% of the mass of the Earth; the outer core makes up about 32% of the mass of the Earth.
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