Ladle crane spill aftermath - video

[Elizabeth Greene]

I would imagine applying water cooling would have a disasterous effect.

It may or may not. The water will instantly flash into steam and increase in volume about 600x. If that steam has a way to escape it's not a problem, like rain on lava. Inside a closed factory it could burn people and melt things.

Once everyone is evacuated you might try misting or fogging to help cool the air and prevent secondary fires, but you definitely wouldn't just hose it down.