Yeah, that's not a bad idea, or at least a few coils as someone else suggested. I've actually got around 60' of 3/4" copper that I'll be pulling out of the house (feeds to old water-filled radiators that we no longer need) - but that's only a little over a gallon if I have my numbers right.
Sticking one of the old radiators on the outside wall of the house and diverting water via that might work (after all, it's only a problem when the weather's hot :-) but then I'd have to remember to bypass and drain the darn thing during winter.
Adding some styrofoam seems like a cheap and quick solution and one that needs no maintenance - it's just down to a question of how thick to make it, how long it'll last, and what to attach it with.
cheers
Jules