Is it possible to hot blue chains for rust protection? I surmise there would be parts of a bike chain that are made using hardened steel (e.g. rollers and pins). Would this process affect their temper? Would cold bluing do just as well?
Excellent question - I know some chains can be bought anodised , so they have a super-thin layer of chemical deposited by electricity. Nickel-plating is done this way.
My first thought is what's already on the chain? If it has any form of chrome or polish then that has to be removed before bluing. Likewise every trace of lubricant or grease would need to be removed else it interferes.
To get a spotless clean you may have to disassemble the chain completely. That alone would put me off.
If you have an old chain handy, it may be worth trying whatever products and techniques you are equipped for. It might be worth trying to cold-blue ~5 links and see how that works.
Given the vertical outer-side plates are the ones most easily seen, you could sand off any existing coating, clean, and then attempt a cold blue. This might leave you with an alternating light-dark pattern.
I look forward to the results of whatever you're able to try.