A Hagedorn temperature in post-inflationary dynamics?

We consider the possibility of regarding the maximum temperature $\tm$ of a plasma of inflaton decay products as a Hagedorn temperature connected with the transition from an inflaton-dominated epoch to a radiation-dominated universe. Employing a ``bottom-up'' approach to inflaton decay, we show that the limiting temperature $T_{\rm H}\sim m_{\phi}$, as obtained from a numerical analysis of the evolution equations, can also be understood theoretically in a Hagedorn picture of the phase transition.