I was experimenting with a lot of materials for making a little backpacking wood stoves about six months ago, and I decided to test them by putting them into the coals in my big kitchen woodstove at home. I wanted to see which of them would withstand the heat of a wood fire.
I had little credit-card sized pieces of various foils (copper, brass, 304 stainless, 309 stainless, 316 stainless, CP4 titanium, CP2 titanium, 6Al 4V titanium, 15-3-3-3 titanium, molybdenum, inconel 718, and inconel 600) in various thicknesses. I also has short lengths of wire/rod in many of the same metals, and I had a collection of glass and ceramic fiber woven fabrics (E glass, S2/Zentron glass, basalt fiber, vitreous silica fiber, quartz crystalline silica fiber, silica/alumina fiber, pure alumina fiber, and zirconia fiber).
Almost everything melted or burned. The heavy inconel wires and the zirconia cloth were the only samples that survived basically unchanged except for discoloration. The alumina fiber cloth survived but became very brittle. All of the titanium turned to ash. The molybdenum and the finer steel wires burned away completely. The heavier steel wires, the steel foils, and the copper and brass melted into little puddles. The glass and basalt fabrics melted, and the silica fabrics turned to dust in my hands when I tried to fish them out the next day.
So, woodfire temperatures vary over an enormous range. Even titanium and steel melt or burn in a very hot wood fire. But in the relatively cool fire in a backpacking wood stove, copper should be fine if it is kept away from the hottest parts of the fire. It might oxidize a bit. If it is a larger stove and you plan to load it heavily and use it for long burns, it might not do so well.