Chemistry - Shea Stearin Extraction by Dry Fractionation

Shea butter is a complex combination of esters:

(Wikipedia). The overall ratio of oleic to stearic acids is about 2/1, but statistically, there will a little of the high melting stearic, more of the 2 stearic to 1 oleic; much more of the 2 oleic to 1 stearic, and a lot of all oleic ester. The melting point of shea butter is low (body temperature) and so if it does not precipitate out the tristearin even at room temperature, you will have to do something different.

A fractional crystallization involving higher temperatures would use a poor solvent for the tristearin (mp ~ 72C), like ethanol. The oleic esters will be more soluble. Make a 20-30% solution in hot ethanol (be careful!!) and let it cool. Experimenting with similar alcohols (propyl, isopropyl, and perhaps with a bit of water added (~5-10%) could give better results.

Oiling out is a common problem in trying to crystallize organic compounds.