[LibWhacker]

Consider two particles approaching each other at some relativistic speed. You can ask what is the temperature of that two-particle system of particles.

As the velocity approaches c, the relativistic mass of each particle approaches infinity:

Which means the energy (and temperature) approach infinity. There is no such thing as a maximum theoretical temperature.

[dr_lew]

Boltzman's constant is k = 8.617 3324 x 10^-5 eV K^-1, and each lead ion has energy 287 TeV, corresponding to T = 3,300,000 trillion degrees. But this is not a temperature, just an energy divided by k. The temperature of the quark gluon plasma created by the collision is about one millionth of that.