Abstract: The facility comprises a tire-building station that is configured to form an uncured tire on a core. A curing station is configured to cure the assembly formed by the core and the uncured tire so as to obtain a cured annular tire. An extraction station is configured to separate, after the curing operation, the cured tire from the core. The curing station has a first, heating, thermal source which presses against the exchange face of the core for the curing operation and is then dissociated from the core and remains in the curing station in order to leave the exchange face free again when the core and the cured tire are transferred to the extraction station so that a second, refrigerating, thermal source of the extraction station takes the place of the first thermal source in contact with the exchange face of the core so as to cool the core.