Driving without serpentine belt - overheating?

Being a Chevy Lumina, odds are it has the 3.1L V6 that came in the overwhelming majority of those cars. That engine is a standard pushrod type with a chain driven camshaft. A few of them came with the horrible 3.4L DOHC engine, the water pump layout of which I am not familiar. I never had the displeasure of dealing with one of those, but have heard some stories.