Temperature is related to average of particles kinetic energy.
I would like to ask about a singular state of a particle system of a little time interval.
The question is:
If all particles were going same direction, same speed, same mass, for that while they were avoiding external forces, internal colision, interaction, etc, then even within this interval they will have an average kinetic energy, so a definite temperature.
But, in this case, I think it's better to describe as a "movement of whole the system", instead of a "temperature of the system", because there is no relative shaking, then I see there is a kind of restriction about particle speeds, they have to be diverse to have a temperature.
I know in practice that's a very unusual process or even a ephemeral one, but I would like to think about theoretical meaning, How is this assumption of speed diversity defined within a gas model ?