A system for sealing thermoplastic film includes one or more bag sealing units, each comprising a lower vacuum platen and a vacuum chamber cover adapted for sealing engagement on the platen to form a vacuum chamber. A sealing bar assembly includes a sealing bar designed for constant heated operation and a pair of cooling plates which function as heat sinks. The sealing bar assembly is pneumatically reciprocated between a raised, disengaged position and a lowered position with the sealing bar engaging the neck of a bag for hermetically sealing same. The cooling plates clamp the bag neck against a sealing support assembly. A method of sealing a thermoplastic film bag includes the steps of placing a packaging object in a thermoplastic bag and placing the bag on a cradle with the bag neck extending over a bag support assembly. Avacuum chamber cover is placed on the platen and evacuated to form a vacuum chamber. A sealing bar assembly melds the thermoplastic to form a sealed area across the bag neck. A cutoff knife blade severs the end of the bag beyond a sealed area, which extends across its neck.