Assuming that the earth is spherical, that its temperature is continuous, and that some other more or less realistic conditions hold, we might think that the Earth's core temperature should be about the average of its surface temperatures.
This is not the case, as the core is hotter than all but a few spots on the surface. Can someone explain where the assumptions break down? Is it that the temperature is not static?
Best Answer
In the limit of very, very long time you can expect that situation to obtain, but
In the time since I first wrote this, David Hammen provided a much more complete discussion of the geothermal heat budget. What you see here leaves off the latent heat of fusions at the inner core boundary and the conversion of gravitational potential to heat as the Earth settles out into density segregated layers.