I do not believe the lead termometers we can afford to buy are exact.
At least here in Italy the strenght of the electricity is not what it should be,it varies during the day,it depends on how much the industries are working.
I have ,I am really wicked;no faith in the thermostats of my pots,Lee,Lyman or rcbs..
I crank the thermostat all the way up,and,as old Elmer Keith said in his books,when a small piece of dry wood burns spontaneously on the surface of the molten lead I begin casting.
Minié bullets cast from so called “pure lead” (another philosofical” concept) need the hyghest temperature your pot can reach,
It depends on the actual strenght your local electricity is.
Actually I like my cartridge gun cast bullets to be a little ,and uniformly frosted.
Optimum for water quenching from the mould.
And optimum for liquid Alox and Xlox lube.
If you fear rapid oxidation of your alloy,you can cover its surface with
wood ashes(old timers trick) or cat litter,farina di Tripoli,aka diatomaceous earth.
And follow LWestoff criteria,when the bullets are good your temperature is OK.