Full Idea
Having a particular average kinetic energy is only a necessary condition for having a given temperature, not a sufficient one, because only gases at equilibrium have a well-defined temperature.
Gist of Idea
For temperature to be mean kinetic energy, a state of equilibrium is also required
Source
Weisberg/Needham/Hendry (Philosophy of Chemistry [2011], 6.2)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.35
A Reaction
If you try to pin it all down more precisely, the definition turns out to be circular.