There is no relativistic limit to temperature. You probably calculated temperature by using the speed of the particle (and assumed it to max out a c), but at relativistic speeds this is wrong, you should use the energy of the particle instead.

The question is: Does particle A impart energy to particle B, or does it take away energy? Whichever is faster imparts energy to the slower one. It makes no difference that the speed is limited - one particle can always have more energy than the other, and can therefor impart energy to it. It's not possible to actually reach that speed, so no matter how fast a particle is moving, you can always increase its speed.

Time dilation should cause some very interesting artifacts though, I have no idea how to go about calculating what would happen. Length dilation is even more interesting - you may find your particles are so small that they pass each other and don't collide.

However it's not actually the particle that collides, it's the electric fields that collide. But electric fields travel at the speed of light - so the fields won't really have time to notice each other.

And finally at these energies a collision is unlikely to bounce, instead it would create some new particles, using up the energy and cooling rapidly.

Technical limitations aside, not really. However, there's the Planck temperature of 1.42×10^32 K where our physical models break down.

The first (utterly naive) guess that springs to my mind would be that at that point the vibration would be sufficiently fast that when sampled at a Planck time interval, there'd be no motion at all. Like overflow of an unsigned int. This is almost surely wrong. :)

According to wikipedia (heh), quark-gluon plasma is not really a plasma so much as a liquid. Presumably, that means the modes are still roughly momentum modes, and you can literally think of a hotter QGP as faster quarks and gluons sliding around and slamming into one another. It's a Fermi liquid, though, which means the exclusion principle has significant effect. (I'm a physics grad student, but not a high-energy theorist, so take that for what it's worth.)

Molecules will break apart above a few thousand degrees. If you take a gas (say Helium) above a certain temperature (probably ~1e4 K) the collisions between the atoms will knock the electrons off and you'll be left with a plasma.

Confining a plasma could either be done with magnets (e.g. a fusion reactor), or with more plasma! (in the case of stars, where the gravity keeps itself from exploding).

Above 1e7 K you start to get fusion of Hydrogen, and I think above 1e11 K pretty much any nucleus will fuse/break down.

So it's difficult to say there's a maximum temperature, as it's quite hard to define.

What's your maximum temperature? About 41'C... above that and you'll die...

Hopefully there is some clarification to explain how I won't die...

BTW, as a teen I remember playing out in the sun at a good 52°C. Don't think I died :)

And yes, these are well above biologically-friendly temperatures. :)