What happens when atoms speed up to extreme velocity? The title might be misleading, but my question is in regard to what happens when we reach temperatures close to absolute zero (Kelvin). I've found different quotes as to what happens on the low end of the scale:

At about 10 micro degrees Kelvin, Rubidium atoms move at about 0.11
  mph (0.18 km/hr) — slower than a three-toed sloth, says physicist Luis
  Orozco of the University of Maryland.

But what happens if we turn it around, and (hypothetically) increase the speed of the atoms to speeds close to c?
 A: The important factor is not the absolute speed of the atoms but the speed relative to each other. I would guess the article on the rubidium atoms is related to making a Bose-Einstein condensate, and slow relative speed is needed otherwise your cloud of atoms just disperses instead of making a condensate.
Increasing the speed of an isolated atom makes absolutely no difference to it, but if you increase the relative speed of atoms in some assemblage the atoms will collide with each other at that speed. As you increase the relative speed from the low levels of the rubidium atoms the collision energy will grow to the point where it ionises the atoms, so the atoms form a plasma. If you carry on increasing the speed up to near light speed the collisions between the nuclei will be so violent that they completely destroy the atomic nuclei and break them into showers of hadrons.
We can be confident about what happens in near light speed collisions, because this is exactly what the RHIC does. The LHC has also done heavy ion collisions in between finding the Higgs boson.
It's worth a note that Tokamak fusion reactors work by raising deuterium and tritium ions to very high relative speeds so that the collisions cause the nuclei to fuse. The corresponding temperature is about 100 million degrees, though from a quick Google I couldn't find the velocities of the ions. You don't get fusion in the RHIC/LHC experiments because the energies are so high that the nuclei are completely blown apart.
A: Collision cross section go to zero for hight velocity. If you try to accelerate electrons to very high velocity, their probabity of collision goes to zero and you create runaway electrons, something quite common in laser plasma interaction.
