Correct. Core temperature of Saturn is around 12,000°C, while the Earth’s is around 6,000°C.
I have never read that Saturn is hotter than the Earth, where did you get that value?
It’s almost impossible to say what is the temperature of Saturn. The highest cloud tops, right at the edge of space, are colder than -150 °C. But as you travel down into the planet, pressures and temperatures rise. At the very core, temperatures can reach 11,700 °C.
http://www.universetoday.com/guide-to-space/saturn/temperature-of-saturn/
Effects
All of this means that Saturn is a frozen planet. The tops of the gaseous clouds average minus 285 degrees Fahrenheit. The temperatures below this hydrogen and helium gas layer are considerably warmer than those at the top, with estimates as warm as minus 20 degrees near the surface. The helium gradually sinking through the hydrogen is thought to create the chemical reactions that make this possible.
http://www.ehow.com/about_4601019_what-average-temperature-saturn.html