Just so ya know, Den, I've saved that picture in my "steam porn" file!
There are any number of coatings (paints) rated for high temperature applications. (e.g. automotive engine spray paint). I suppose there may even be specialized powder coatings that are rated for high temperature. However, I believe that traditionally the coating of choice for fancy cast iron engine parts was "stove enamel" or "porcelainizing," such as one still finds on fancy French cast iron cookware (e.g. Le Crusette brand). This stuff was much more common in decades past, being used to coat just about anything that would get hard everyday use and might rust. (Like those speckled blue campfire coffee pots people use to take camping a long time ago or the old fashioned white hospital basins and pans in use before stainless steel was common.) (Oskar Schindler supposedly operated a cookware factory turning out porcelain coated goods and there's a scene in the movie "Schindler's List" showing workers doing it.) It's still used on top end woodstoves, such as the Vermont Castings line and on expensive cast iron bathtubs. It can still be done, but you'll have to find a shop that does it as piecework. Basically, it is porcelain slurry that is applied to the piece, which is then fired in a kiln. The result is a tough glass-like smooth glossy coating of porcelain on the iron piece. There is a drawback, though, in that if a piece is dropped or struck hard with a tool, it can chip and cannot be effectively repaired without entirely recoating the piece.
As for bright finishes, I don't believe that chrome electroplating was as common back in the day as was electroless nickel plating, a chemical, rather than an electroplating process using electrical current. Electroless nickel plating, about which I don't know much, produces, to my eye at least, a deeper, slightly less garish, and much more durable bright metal finish than does chrome plating. (It's often encountered in the restoration of older, top end classic cars and other pre-WWII items, after which it was supplanted in the industrial arena by chrome electroplating which was cheaper and easier, although less durable.) There is also nickel electroplate, which has the same limitations as chrome electroplate, when compared to the chemical plating processes.) Chrome electroplate is plenty good for most purposes, if applied thick enough to last, and a chrome plating shop is a lot easier to find these days than a nickel plater, but nickel, rather than chrome, is what you'll find on the old stoves, for durability considerations, I'm guessing.
I believe the iron parts of the famed Beaumaris (Mills) engines were coated with stove enamel and the steel parts nickel plated. Together, treatments like stove enameling and electroless nickel plating produce a very subtle but unique "classic aura" that cannot be truly duplicated by modern techniques.
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Den