Satan does indeed mean temptation, but it is the temptation to regard malignancy as something outside of and influential upon human nature. Malignant, evil, demonic, monstrous…these and many others are just the names we use for different malformations of the natural human being. Dogs have it in their nature to be vicious or loving, humans much more so.
The temptations Jesus confronted in the wilderness are those that confront people by virtue of their imagination and sociability. We can imagine worlds in which others regard us more highly, in which the world yields to our tools, in which we shape our destiny…and that imagination in the context of sociability creates endless new channels into which our animal nature can pour. That’s why everyone, sinners and saints alike, except by the grace of God, becomes the King or Queen of an imaginary world and rules there, the way an author rules his characters, or a child his sand castle.
Jesus did not overcome those temptations. He died to them. That is the narrow way.