Yor_on, BC might not be terribly diplomatic, but he has a good point. Coming up with a new definition of temperature isn't inventing a new physical theory. Temperature is a tool for approximating values of things, and redefining it is breaking it's ability to make useful approximations.

**Temperature is not a fundamental property of matter.** It's an average value (of kinetic energy) that's useful because when you're dealing with billions upon billions of particles, you can't hope to solve the equations of motion of each particle to describe how the system changes in time. Instead, you write a theory in terms of average values, which is much easier. **This is essentially the entire point of temperature: it's the average kinetic energy you'd get if you solved the equations of motion for all the particles in your system, and therefore the definition of temperature and it's properties are derived from the equations of motion for those particles.**

Dealing with sub-Planck length temperature effects is pointless, since there are no valid sub-Planck length equations of motion (yet). As the laws of motion are extended to to sub-Planck lengths, temperature will follow. But temperature can't go there first, since it's defined from the laws of motion.

The same goes for the arrow of time: fundamental laws of motion don't care about the arrow of time^{*}, so temperature can't depend on them. If you want to include the arrow of time in the definition of temperature, you first have to show that the fundamental laws of motion depend on it.

Absolute zero is also not a special, fundamental property of matter. It's a name we have for the case where all the particles being averaged over are in their lowest possible energy states. If you're averaging over classical mechanics, this means nothing is moving at all. If you're averaging over quantum mechanics, there's the possibility that things are still moving, since the lowest possible energy for quantum particles is sometimes not actually zero-energy.

Zero point energy, again, isn't anything special, nor it it related at all to the definition of temperature. It's just the name for the lowest energy state of a quantum particle, which often has non-zero energy.

Again, to reiterate: temperature is a tool that's designed to simplify solving the equations of motion. Temperature's definition will change as the laws of motion change, not the other way around. If you change the definition of temperature without changing the laws of motion, then temperature becomes useless: it can't simplify your calculations anymore, and it is no longer related to the laws of motion or physics going on.

-------------

* With the possible exception of CPT violation...