The method includes at least the following steps of spraying a flow of sterilizing vapor, including a vaporized sterilizing product, towards the preforms to be sterilized, so as to cover at least an inner wall (15) of the preforms to be sterilized with the product and heating, by radiation, the preforms covered with sterilizing product in order to bring them to a temperature (T2) at or above an activation temperature (Ta) for the product. The spraying of the flow of sterilizing vapor is carried out in a protective chamber (40), heating is carried out outside the protective chamber (40), and the flow of sterilizing vapor is in the form of a jet of vapor (F) vaporized onto the preforms (12), in such a way as to bring about the deposition, by condensation, of a substantially uniform film of condensate (48) of sterilizing product on at least the inner wall (15) of the preforms to be sterilized.
