if you want it white, you should probably use a lot of coconut or palm oils, and you can add kaolin to help the whiteness.
Mine never turn out completely white either, because I use a lot of OO. The only one I got completely white was the salt soap I made with 90% coconut oil.
you mean "hot process"? ive made some that were white, use the lightest oo you can find, also the fo has to have no vanilla, that will discolor your soap, most fo places will tell you if it has vanilla, at least natures garden does.