A Hagedorn temperature in post-inflationary dynamics?

We consider the possibility of regarding the maximum temperature $\text{tm}$ 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 $T_{\mathrm{H}}\sim m_{\varphi }$, as obtained from a numerical analysis of the evolution equations, can also be understood theoretically in a Hagedorn picture of the phase transition.