Does temperature in static particles increase due to gravity?

[Felian]

Hello, I was wondering if particles that have a set position such as for example particles within the earth's core would experience a temperature gain due to gravity.
If kinetic energy is applied to the particles in the air due to gravity, then kinetic energy should also be applied to particles deep inside the earth right? But because the particles don't really have anywhere to go I would expect this kinetic energy to be transformed into temperature.

If so, how do these gains in temperature differ based on distance to the core? The total force of gravity would be higher in the core because its average distance to other particles would be lower, but the forces do balance out completely at the exact core because it would come from all sides. How would these forces translate into thermal energy?

 

[JeffKoch]

I think you are confusing gravity, density and pressure. The net central force of gravity decreases as you move closer to the center of the earth, but the pressure, density and temperature all increase. How exactly they do this depends on how far down you go, what the local material composition is, and what it's equation of state is.