It’s an interesting question, but a bit vague. Even at room temperature, relatively needs to be considered for the motion of electrons.
You’re probably thinking about bigger stuff though. The short answer is that temperature is unbounded so yes, there is a temp at which it is significant for the motion of all particles. I think inside of stars this can happen, but my knowledge jn that area is pretty limited.
Veritassium has a recent video about some of this that you may find interesting if you haven’t already seen it.