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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.
Temperature is a measure of kinetic energy at the molecular/atomic level. That said, the gasses falling into a black hole would likely reach such hypothetical temperatures as they near the event horizon.
But what about cutting steel with a plasma torch? Could you see macroscopic results of particles doing counterintuitive quantum stuff?
Certainly! You can see discrete emission lines from the ionized air molecules, which only occurs because of quantum physics. I realize that’s not what you’re asking though.
I did a quick calculation and for a plasma torch (~27000 Kelvin) and assuming air molecules, the average velocity of the plasma ions would only be like 6000 m/s. That’s 0.001% the speed of light, so you aren’t going to see any relativistic effects.
So… no superposition, entanglement, tunneling or teleportation in macroscopic scale. ☹️
Sorry, physics can be cruel sometimes :(