Oxidization is a chemical reaction, so chemicals would be necessary for removal, not just heat. Gameplay is better than realism, but in situations like this, Mojang typically makes realistic additions. (Think changing cookies to seeds for parrots and when anti-oxidation was added in the first place.)
From a bit of research, I see that most of the cleaning is done through pastes or juice rather than heat. It'd make sense if some sort of water and honey combination could clean it. Most likely, I'd say you can craft a water bucket, honeycomb and rusted copper block together to reset its rust state with the water bucket not being consumed upon crafting.
But the Furnace doesn't seem to just use heat, and the fact that it can smelt ores indicates that it can be used to reduce metal oxides, as most ores are either oxides, carbonates, or sulphides (And rusted copper itself in-game rusts into the carbonate, which IRL is, as malachite, one of the main copper ores), so, if the furnace can smelt ores, it should be able to remove rust.