Couple of metalurgy points. The color is very closely related to the maximum surface temperature it experiences after being polished. As we know, the color is caused by the iron oxide (rust) layer/film thickness. Since the rust layer tends to protect the iron in the steel surface from further oxidation, the rust film is thickened much more by higher temperature than exposure time. Consider bluing. The color is caused by a "black" rust film that is not thick enough to totally cover the surface; that part of the light reflected appears blue due to the thickness of the film. If we chemically force the film thickness sufficiently to block light reaching the unrusted surface, the color will appear black (the actual color of the rust; the surface absorbs all wave lengths/colors of light and, therefore, appears black).
So, the objective of fire coloring is to raise the surface temperature of a highly polished piece of steel to the temperature that produces the desired color; see linked chart above. It really doesn't matter how you achieve the temperature. Some of the above recommended chemical additive (like dipping in oil) may increase film thickness. Sans chemicals, it is all about polish and temperature.
There is no benefit in quenching or not quenching the fire colored part. The benefit of tempering a heat hardened steel part (assuming the part is made of steel of sufficiently high carbon content, say above 0.3% carbon, to respond to heat hardening) is to trade some loss of hardness for a substantial reduction in brittleness. There is no such thing as temper for low carbon steel parts. Do not confuse the surface "colors" with the heat treat or case hardening processes.
DDA
