There's normally a transmission cooler in one of the radiator tanks. Sounds like it has corroded through. Have the cooling system and transmission flushed after replacing the radiator. Petroleum products in the coolant will rot the rubber hoses from the inside, but more importantly, antifreeze doesn't offer the right friction characteristics and seal conditioners needed in the transmission.

Answered by caradiodoc (expert)
17,285 answers provided

Cardiodoc is spot on with this, these commodores are known for this problem, make sure you get a top quality radiator new radiator and do the flush as mentioned, the commodore transmissions do not like coolant in them at all, i would be getting a total trans flush as well.

Answered by mhpautos (expert)
26,913 answers provided