What are the odds of getting a Shea Tree to grow in South Carolina, USA? Temperatures here in SC range from mid 30s (occasionally around 40) Centigrade in the summer to -10 at the coldest days of the winter. There is usually consistent rain so that oaks, peaches, and apples grow easily. The soil is mostly mildly acidic clay and sand. There is a eucalyptus tree in our yard which grows fine but not terrifically.
In gardening (nearly) everything is worth a try (IMHO). If you're successful you will learn a lot! and enjoy great satisfaction. Even if you're unsuccessful you will still end up learning a lot! from the experience.
That said, the tree you wish to grow is of good (final) size, won't be able to bring it inside during your cold winter months, and will take many years before producing nuts that can he harvested (if that is your ultimate goal). Also your growing conditions are going to be very! different from its native habitat "West Africa".
Before making a final decision on whether you wish to invest the time into such a project, I would seek some expert advice from horticulturists that are located in your specific area of the country. Since moving to the USA I have found local (cooperative) extension offices to be an excellent place to start:
Here's a (other) reason why you might want to contact your county (local) and/or state government or local Cooperative Extension Office and seek their advice:
I am not for one minute saying your particular situation, or county and/or state government falls under the above. I'm just making you aware of something I heard one more than one occasion.