A plant for making containers of thermoplastic material in continuous cycle comprises: a rotary molding machine (1) configured to make parisons (2) of thermoplastic material having a body (3) with a closed bottom and a neck (4) which defines an opening; an oven (5) for heating the parisons (2), connected to the molding machine (1) and equipped with heating means (6) operating on the body (3) of the parisons (2); a rotary blow-molding machine (7) configured to receive the parisons (2) heated in the oven (5) and to blow-mold them in molds (8) to make the containers; and a management unit (9) for the plant (10), configured to switch off the oven (5) heating means (6) during a shutdown period of the blow-molding machine (7) but without interrupting the operation of the molding machine (1), so as to enable the parisons (2) located in the oven (5) to cool down during their transit through the oven (5).