What happens when frozen Jello melts?

Capt_Bloth and I want to make Jello in a hurry. He thinks that we should use not only the quick-set method of adding ice cubes, but also put the pan in the freezer. Now, I think this has the potential to freeze the whole pan. What’s the problem, you – and he – say? Won’t the frozen Jello just turn into a jiggly gelatinous mass once it hits fridge temp?

I’m thinking not. I think that once it unfreezes it’ll just liquidate into Kool-Aid. Maybe this is how they make Kool-Aid?

Can’t find anything on the internet. What say you, jello-expert jellies?