I am starting to think our temperature scale is upside down. Colder temperatures should be larger, and hotter temperatures should be smaller. This definition of temperature still satisfies the requirements of my previous post: relative temperatures still tell which way heat flows, and the ratio of two temperatures still determine how inefficient a heat engine would be.
The third law of thermodynamics is thrown away because it is now the obvious statement that you cannot cool an object to an infinite temperature. It also becomes clear that negative temperatures are ultra-hot, and not ultra-cold.
Of course, to not to be confusing we need a different name, like cryoture. Time : Frequency :: Temperature : Cryoture. Then we need a scientist to name the units after, like one boltzmann is the cryoture of the triple point of water.