My idea is simple.
I assume a cooling mechanism in the physical world is emission by light. That is. Energy (light) removal from a body.
A thought experiment would then be that physical bodies emit invisible light dependent on its kinetic energy.
I guess this because if there is a maximum velocity for mass then any energy input that would result in a higher kinetic energy would have to be removed.
The fastest way to remove energy is by light. Hence bodies should be able to emit a kind of light dependent on the velocity.