  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.
