To feivel,
I figuered you were talking about a klei shelishi, but even so this psak is not so pashut. First of all, not everyone holds the ladle is a keli. (Even though most people are Makel.) (Look up Shulchan Aruch- Hilchos bishul.) Second of all, there might be a problem of Nolad – to melt the ice cube (changing its’ matter state). You are allowed to do Nolad for a Tzoirech godol, but I’m not sure what the Tzoreich godol is here since you can cool it off by putting it into the fridge or freezer.