The new temperature is about as hot as the Sun's surface and the team from University College London believe their figure is the most accurate yet achieved.
Volcanoes reveal the Earth's internal temperature
"Its crucial to know the temperature of the Earth's core," explained Professor David Price. "There's tremendous heat energy stored down there and the heat flowing out of the core causes earthquakes, volcanoes and the drift of continents.
"It also causes the turbulent swirling motion of liquid iron in the core that creates the Earth's magnetic field. But if you don't know the core temperature you just can't understand how this all works," he said.
The team used a Cray T3E supercomputer to make a remarkable calculation of the melting point of iron, the predominant element in the Earth's core.
The Earth's inner core is solid, whereas the outer core is liquid, so the melting point of iron is a good indication of the temperature.
"If we know the melting temperature of iron at the pressure of the boundary between the solid and the liquid core, then we know the temperature of the Earth at that boundary," team leader Dr Dario Alfe told BBC News Online.
The new "ab initio" calculation was explained by another team member Professor Mike Gillan: "By using the basic laws of physics you can model any material as a collection of atoms and calculate the melting temperature - and anything else you want - completely from scratch."
The key to the calculation was predicting the melting point at the crushing pressures which exist at our planet's centre, 6,370 kilometres down.
The big squeeze
Previous estimates of the temperature have been made by trying to simulate these ultra-extreme conditions in the laboratory, but the results have varied by over 2,000°C. The UCL team claim an uncertainty in their figure of plus-or-minus 600°C.
The team calculated the melting temperature of pure iron at the core to be 6,400°C but the 10% impurities of nickel, sulphur and other elements reduce the figure to 5,500°C.
"The idea that we are sitting on top of a seething mass of molten iron as hot as the Sun may be pretty scary," remarked Professor Mike Gillan. "But scientifically the core temperature is important because it is a crucial in understanding how the Earth changes over time."
The research is published in the journal Nature.
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