What is the motion of the earth that is responsible for the cooling at a rate of 100 degrees Celsius per billion years?

Answer 1

The only way the earth is going to cool because of its motion is if it moves away from the sun. Another possibility though is that the sun will cool.

Answer 2

The motion of tectonic plates on Earth's surface, known as plate tectonics, is responsible for the cooling of the planet at a rate of 100 degrees Celsius per billion years. This process involves the movement of Earth's outer rigid shell, leading to the formation of new crust at mid-ocean ridges and the recycling of older crust through subduction zones, ultimately helping to dissipate heat from the planet's interior.