The Libellus de Alchemia, by pseudo-Albertus Magnus (Sister Virginia Heines translation) has a short chapter on the preparation of alum to be used in the alchemical work. All you do is put it in a crucible and stick it in a furnace, heating slowly at first then afterwards strongly and allow it to dry through a day at full heat. When cool remove it, it’ll be snow-white and is used for making the liquid for whitening.
Obviously I can’t stick a camera inside a furnace. The recipe is a little unhelpful as well as to the temperature, but since it describes the building of a wind or natural draft furnace in some detail atthe start, you must expect temperatures of over 900C.
Which can be reproduced by a blowtorch, hence this video:
Note that thanks to the large amount of water locked up in the crystals with the metal sulphates it melts first, before the water boils away.
The white stuff is the puffed up mixture of potassium sulphate and aluminium sulphate, although it is likely that since the aluminium sulphate breaks up around 700C, it’s a mixture of aluminium and potassium sulphate, which melts at 1069C, a temperature my blowtorch won’t really reach, or rather, despite the flame temperature being higher than that, it isn’t putting enough heat into what it hits to be able to melt anything that melts at that temp.
Anyway, that’s what happens when you make your snow white calcined alum.
Now in modern times we know alum is useful as a fire retardant, but beyond some ancient Greek mentions I haven’t found anything about it being so used in medieval Europe.