I am planning on writing a research paper in my high-school physics journal on analysis of high temperatures, and possibly, a bound for an "absolute hottest temperature" (depending on the type of material). I have been using the Maxwell-Juttner speed distribution to analyze a few calculations under the assumption of monatomic gases (such as Hydrogen and Helium). So for example, calculating the temperature of one mol of H2 (assuming S.T.P. conditions) with the M-B distribution, where the most-probable speed would be v = 0.99c. I've been trying to see if there is a limit. I know some conventions have been the Planck Temperature, since our theories don't work beyond that. however, I've been trying to find a better way (or I guess, abetter justification) for analyzing perhaps bounds on extremely high temperatures attainable. I do know that at really high temperatures, quantum effects take place, and things like degenerate matter are prevalent, or stuff such as quark-gluon plasma. Additionally, I was wondering - how do I consider pressure under the Maxwell distribution? Does the equation change with pressure? Could anyone provide me with some suggestions as to how to proceed with these research ideas? Thanks, I really appreciate it.