On the definition of the measurement unit for extreme quantity values:   some considerations on the case of temperature and the kelvin scale
  Many quantities are attributed a range of values that can apparently extend to infinity (on one side or both sides). In this respect, the definitions of their measurement units do not place any constraint to the maximum (or minimum) value for their validity. In general, that happens because those extreme values are far from being reached on the earth, or presently in experiments. However, since the same units are used also in fields of physics, chemistry or technology where they could occur, namely in the description of the universe in one sense, and in nano-scale or particle physics in another sense, the issue of extreme values (not in statistical meaning here) is not irrelevant. The question placed and discussed in this paper is whether the present kelvin scale, based on Lord Kelvin second definition (our currently accepted concept of temperature), applies over a full range between bounds (zero, infinite) or not, and about the concept of temperature in itself in the extremes regions. The aim, however, is not to provide an answer, but to suggest there are difficulties with the application of current concepts at extremes of temperature. 
Franco Pavese
physics.gen-ph