Why doesn't the heat of the Earth's core diffuse to the surface? The Earth has a crust, mantle, outer core and the inner core with each one getting hotter than the next. How come, over millions and millions of years, the heat that is at the center of the Earth hasn't conducted throughout the planet's material so that the entire planet is one even temperature? 
This always bothered me because we all learn that temperature diffuses from high areas to low areas, yet the Earth's center is super hot while if you dig a one foot hole, the ground feels quite cold. I never understood this. Thoughts?
 A: It's a bit like when you put a thick jumper on. The inside of your clothing ends up being warmer than the outside of your clothing.
Most of the heat within the earth can be attributed to radioactive decay (of long lived isotopes like potassium). This heat is constantly being conducted out to the surface. (Yes, if you go down into a deep mine, you will get hotter.) It turns out that kilometres of rock works as a reasonably good insulator.
Remember that the difference in temperature affects how quickly heat is transferred. If the surface was nearly as hot as the interior (like when it originally formed) then the surface would radiate heat into the cold night sky much faster, and the crust would conduct internal heat away from the core to the surface even slower, and this imbalance would cause the surface to lose net thermal energy and cool down (while the core heats up even further); this process continues until an equilibrium is reached (where each layer of the earth has its own roughly stable temperature, and each layer is getting rid of excess thermal energy at just the same rate as it acquires it).
A: The pressure at the core is higher, so higher temperatures are thermodynamically more favourable there.
More importantly, the Earth is not in thermal equilibrium. Heat can't move outward from the core nearly so efficiently as from the surface off the planet, for example, so the surface cools a lot more quickly. 
There are also mechanisms which continue to generate new heat deep underground, but not at the surface: friction from the motion of material under the surface, and decay of radioactive elements there.
A: Earth's core is losing energy to the universe. Just very very slowly. Also radioactive elements in the mantle and the core heat up Earth's interior. Also the friction of infalling material to the core adds heat to Earth's core. Also all those layers of rock prevent Earth from losing heat.
A: Gravity continues to generate energy. At the surface that heat can dissipate easier than at the core. 
