What is temperature?

In daily use, the concept of "Temperature" is identified as the measurable "degree of heat" of a substance. Here we encounter already different temperature scales: From Fahrenheit, Celsius C°, etc. , up to the scale expressed in Kelvin.  As a consequence of the second Law in thermodynamics there exists in fact a lowest temperature (but seemingly no highest one). In thermodynamics, the concept of a temperature is introduced as a native state variable associated with the change in the amount of heat as a function of  a related change in thermodynamic entropy. In the framework of classical statistical physics we have the "Equipartition Theorem"  according to which each energy-carrying degree of freedom possesses on the average the same thermal energy. Matters become more complex on the atomic scale, encountering the regime of quantum dynamics where this "Equipartition Theorem"  loses validity.  At small scales, notions such as work,  heat and temperature need to be reassessed. Also, does temperature eventually fluctuate ?  These issues become even more obscure when describing the influence of the theory of relativity. Even among experts it is then often unclear what the means are for measuring the temperature of a fast moving system: Is  a moving body now hotter or colder, or does it maintain the same temperature?