But heat is conductive. Why isn't the cooler material heating up as the heat conducts its way away from the core?
I know earth is a good insulator, but after the amount of time the earth has been around, and given the vents we have (volcanoes, etc), if the core were really heating the planet to the temps suggested, we'd never have winter, or polar ice caps.
Don't get me wrong, I know the core is warmer than the surface, but to those temps?
Heat is actually being conducted up from the deeper layers of the earth, and it also comes up by convection currents within the mantle. This heat flow can be measured. The greatest heat flow (on a large scale) is found along the mid-ocean ridges, where new crust is form by upwelling convection currents in the mantle (the layer between the core and the crust). Since the heat is generated at depth and lost to space at the surface, the surface is cooler than the interior.
Think of the furnace in your house. It's a lot hotter than the interior of the house, and the house is cooler than outside (assuming it's winter).