You are talking about TC in direct conduction, not radiant heat transfer, right? I don't see it having a measurable impact, unless you are talking about a thin film of Cu. If you are dealing with a heat tint film that is measured in angstroms it will not impact bulk properties. If your oxide fill is thick enough to be dark and porous then it may have a significant effect. The TC of copper oxide is about 1/20 that of the metal.
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Rust never sleeps
Neither should your protection