B Thought Experiment: Does Gravity's Compression Warm an Object?

[Cayman]

TL;DR Summary

Thought experiment and question concerning whether gravity causes a permanent temperature increase in matter.

Thought experiment:
(1.1) You have a homogenous object, made of one element, floating in space.
(1.2) Gravity has completed the process of accelerating its atoms and molecules into the final state, such that the object is a crystalline sphere.
(1.3) Gravity continues to act on the object, even though the atoms and molecules are now in positions that gravity cannot overcome or move.

Question: Does this object:
(2.1) cool to the temperature of the surrounding space or
(2.2) remain warm for ever due to the eternal compressive force on the object due to the eternal acceleration of gravity on its atoms and molecules?

Asked two other ways:
(3.1) Does compression always warm an object at any scale, even when the compressive force fails to move any of the object's atoms or molecules?
(3.2) Does the existence of matter always imply a temperature greater of the matter than of the surrounding space?

Follow-up question:
(4.1) If gravity occurs in pixels (quantum) and in waves, then this would suggests that, at some sufficiently small scale of time and space, gravity acts in pulses of squeeze and release. If so then would this contribute to an effect of "working" on a crystal, similar to warming up glass by bending repeatedly without breaking it?

 

[phinds]

Summary:: Thought experiment and question concerning whether gravity causes a permanent temperature increase in matter.

Question: Does this object:
(2.1) cool to the temperature of the surrounding space

Assuming it was not near any heat producing object then it would cool down to 2.725 degrees Kelvin