Is anodizing of mixed metals (aluminium and cooper) possible?

I'd like to blacken my [Noctua NH-P1](https://noctua.at/en/nh-p1) passive cooler, made from an aluminium fins and copper heatpipes. Since thermal dissipation is key in my build, I thought about anodizing it, instead of spray paint coating.
The tutorial for aluminium anodization I found on [Wiki-How](https://www.wikihow.com/Anodize-Aluminum) looks quite straight forward, but since my knowledge in chemistry is quite basic, I do not know if and how the heatpipes would interfere the process.
In my case, **not** coloring the cooper at all, would not be a problem, but damaging the heatpipes (which are not solid, but filled with some liquid for ensuring an even better heat transfer) or breaking the soldering between the heatpipes and the cooling fins or even risking to do so, would be a total deal-breaker.




There are two separate ways to color copper and aluminum chemically.


Aluminum and titanium are easily anodized in an acidic water bath. Once anodized, the surface aluminum oxide becomes porous and can be [dyed any color, or it can be colored by interference of light through the anodizing process](https://www.saf.com/faqs/how-do-you-color-aluminum/).


Pure [copper cannot be anodized](https://sciencing.com/methods-plating-stainless-steel-8741267.html), though some Al-Cu alloys can be. Instead, copper can be [colored by oxidizing (torching) in air to produce interference colors](https://www.youtube.com/watch?v=nQJ_Edt7ORw). However, unlike the *very* hard aluminum oxide ($\ce{Al2O3}$) coating of anodized aluminum, copper oxides are soft and absorbent, so that touching the unsealed surface leaves fingerprints. The video link also describes sealing the oxidized surface.


Copper can also be [colorized through chemical baths and other processes](https://www.getty.edu/publications/virtuallibrary/temp/9780892366385.pdf). Sulfides can produce browns and blacks, for example. Note that some of the chemicals used, such as ["liver of sulfur"](https://en.wikipedia.org/wiki/Liver_of_sulfur), are toxic and are not suggested for use at home. Again, a coating to protect the surface is needed.


Since this is to be done to a heat transfer device, though, consider that any coating will reduce cooling efficiency. The thicker coating needed on copper might be more problematic. If there is *sufficient extra cooling capacity*, though it might work.


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