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. For the case of single field inflation models, 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) less than or similar to 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.