I once saw an engraving of a traditional horn shop and the index listed an Oil kettle, I take it it was used to soften horn. A lot of guys use it today, see dogface's reply above.
I use water, I am to messy to have hot oil in the shop, I do a lot of wood working and oil and wood do not mix well.
Never tried a heat gun either. Put the horn in a pot let it boil for awhile, test it to see how flexible it is. Once it is to your liking put a sizer in it, I drive them in with a rubber mallet and let cool. Sometimes they stick but a good rap on the floor will free them.
Another, "To each his own".
Tim C.
PS: My shop is in the basement and I boil them all in here, a little different smell but you get use to it.TC