re: You still have to deal with the limit known as" C".
On that, nick basically had it right--theoretically you could get an answer by accelerating the particles to 99.99999 percent of light speed, but the word "temperature" would long ago ceased to have any valid meaning. It's kind of like wondering about hypersonic velocities on the freeway. It's physically possible, but all the ordinary rules break down.
The hottest Planck temperature was about 10^32 during the Big Bang.
That's probably the maximum possible in normal existence since energy levels have evened out since then, and to get anything hotter than that, you'd have to impart energy/heat to it from something "hotter," and of course, you won't find anything like that.