  We consider the conditions for the decay products of perturbative inflaton
decay to thermalize. The importance of considering the full spectrum of
inflaton decay products in the thermalization process is emphasized. It is
shown that the delay between the end of inflaton decay and thermalization
allows the thermal gravitino upper bound on the reheating temperature to be
raised from 10^{8} GeV to as much as 10^{12} GeV in realistic inflation models.
Requiring that thermalization occurs before nucleosynthesis imposes an upper
bound on the inflaton mass as a function of the reheating temperature, m_{S} <
10^{10} (T_{R}/1 GeV)^{7/9} GeV. It is also shown that even in realistic
inflation models with relatively large reheating temperatures, it is
non-trivial to have thermalization before the electroweak phase transition
temperature. Therefore the thermal history of the Universe is very sensitive to
details of the inflation model.
