Far as I know, Steel heated up into the range where 'colors' begin crawling, as was well known to Blacksmiths or related, if quenched or cooled 'there', the colors remain.

If this is done in an Oxidizing ( Oxygen excluding ) Atmosphere, likely the Colors remain a little better or will occur or remain more vivid or are not going to be interfered with by any formation of Oxides.

Mineral or Metallic Salts ( 'Bone', is refractory, and, though made up of compounds, is none the less, essentially compounds of Metals and other elements - Calcium, Mangnesium, Boron, Phosphorus, Manganese, etc, are Metals ) or Organic compounds can contribute to or occasion nuances in a thin or molecular layer in how they may combine Molecularly with the Steel at Heat.

This then would be the pragmatic basis for any Heat related Blueing operation - an Oxidising Atmosphere, a way to controll the rate of rise, the terminal plateau, and then dissipation of the Heat, and, the introduction of whatever Compounds as will molecularly combine with the surface of the Steel to produce new compounds which then occasion premenent nuances in the Color of that Heat, which basic Color will be occuring anyway.

One can obtain a vivid 'Fire Blue' merely by evenly heating a piece of Steel in the open Air and letting it cool...for that matter. But I will guess, that it will not likely be quite as durable as the Blue which is in effect protected by discrete Compounds molecularly bound into the surface of the Steel.