The earth would not “burn up” if it touched the surface of the sun; it would vaporize. The earth is not destroyed by the high temperature in the core because there are thousands of miles of cooler material between the surface and the core, and because the extreme pressure in the core prevents vaporization.
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?
Good explanation, and might I also add that there is a difference between temperature and heat. The heat of the sun is millions of times higher than the core of the earth.