Why are temperatures on the globe getting colder where it is furthest from fault lines? Is the earth warming from its inner magna core?

You mean tectonic plate boundaries. And yes, tectonic activity is influenced by the movement of material within the mantle and core, and can in turn influence global climate change. But this it does by influencing ocean currents more than anything. VEI 6+ volcanic eruptions can cause temporary climate changes, but the effects are quite short lived. They can, however, give an incorrect baseline if you choose the same decade as a VEI 7 eruption to start your in-depth climate studies (we've been tracking global climate since the 1880s and our baseline comes out of a cooling period that followed the eruption of Krakatoa).

I would love to see the link to valid scientific reports or articles that state the Earth is getting colder where its furthest from fault lines.

Global warming has nothing to do with tectonic plates.

huh? where did you get this info? do you have a reference?