For small parts of clocks I use a tin half full of sand , heated from below and droped in oil as soon as the right color is reached , or tinmans solder is the same temp as blue steel , oil blacking is a higher temp droped into the dirtyist
engine oil you can find and lasts longer than blueing .
Quite the opposite most non synthetic oils burn around the 130 to 160 degree mark, Whale oil 150 degrees.
To turn steels blue your looking at least 265 degrees and by 280 degrees its very light blue.
Also no need to place on sand that only disperses the heat making it more even once eventually warms up.
Blow lamp direct quite adequate and dump in anything to cool, good enough for Purdeys.
Hot browning, sorry blacking or blueing may not take to the steel its made from. Usually a low quality works better. Book linked to above I have here borrowed from a mate in 1992, nothings been available for 70 years or if it is you will be refused supply of some highly restricted chemicals. Proper quality salts are available over here from £40 a bag to £120 going back 6 years.
Assuming the item is made from steel best option take it to a metal finishers, its not worth the hassle. Horrible job any way.
Cold blacking is around 100 degrees parts have to be boiled repeatedly mainly for quality English shotguns where you don't want the barrels to part as they are soft soldered. Easy enough to do and can still give a highish gloss dependant upon the preparation.
Kits you get are mostly a waste of money, so are the cold blacking stuff ok for touching up screw heads.