Copper is very much NOT recommended for amphibian enclosures. I can quote you some information from the Amphibian Medicine and Captive Husbandry book, if you want to see a solid reference. My advice is don't do it.
But that leaves you with a problem: finding a material that is a good conductor of heat/cold AND is amphibian-safe. I've given this problem a lot of thought in the past, and unfortunately I didn't come up with any really good ideas. You can use plastic tubing for heat-exchange, but it's a pretty poor conductor of heat - you'd need a lot more coils of it. Stainless steel would work, but I don't know where you'd get stainless steel piping. Glass would work, but it's too fragile for this application.
Let us know what you come up with!