I have always understood crucibles to cool down at a fixed rate of K/s when no heat is being added, and if any heat is being added, then the heat is added to the total mass of the crucible plus its contents and divided by that mass to come up with the new temperature. I have been using a large steel crucible for some weeks now enjoying this effect by using a fluidized bed invar burning box to heat it up to melt the contents, then switch to a regular invar burner to very gently continue to warm it, mostly just to stop it from cooling off while adding as little additional temperature as possible. Tonight I did a double batch of 140 magnetite + 30 carbon => iron, let it heat up to 2011 to become wrought, then added 40 nickel, let it get back to 2011 to be sure that all of the nickle had merged with the wrought to form 120 invar, then added 10 manganese and chromium to make 90 stainless steel and leave the remaining 90 invar to pour out as invar.
I opened the 6 hoppered redstone controlled auto pouring molds and switched from the fluidized bed to the regular burning box to keep it from cooling down and the temperature continued to drop. Eventually all of the invar poured out just as the temperature fell to 1940 so the stainless solidified. It sat there bouncing between 1939 and 1940 before I lit the fluidized bed burner again to get it back up and pour out the stainless.
Why did the temperature continue to drop despite adding 16 HU/t to the crucible?