Kashering copper and stainless

Question

I need to kasher a fleishig pot that is stainless inside and copper on the outside with a long brass handle. I believe it would fit in a larger pot but I believe it would ruin the pot to boil it in a larger pot and then immerse in cold water. It was a gift and very expensive. If its what I've got to do I will, but first want to make sure there are no special rules with regards to this type of combination of materials, and if I must immerse in cold water immediately? Thanks very much.