Basically, as particles approach the Hagedorn temperature they bleed off energy in the form of matter (hadrons). This process prevents the temperature from increasing, unless it is a quark plasma - in which case there is a second and much higher temperature. The plasma would arise due to degrees of freedom (which is what temperature actually measures) - matter would have an overwhelming freedom to break apart (which it does normally all the time: see nuclear radiation).

So far as I understand it.