Inconceivable means "incredible," "incapable of being explained," "incapable of being conceived or visualized in one's mind": "It is inconceivable that he would have done this to me." "It is inconceivable that water should not be wet." Unthinkable refers to something that cannot be made an object of serious thought, but the word is more often applied to matters that are improbable or difficult to accept: "It is unthinkable that he would have left me no money for food." "No matter what the minister says, I consider eternity to be an unthinkable subject."
Dictionary of problem words and expressions. Harry Shaw. 1975.