what is Caesar's opinion of himself in Act III Scene 1?

His opinion of himself is that his public self is so strong that his private self cannot be harmed.

Sparknotes analysis;

compares himself to the North Star, which never moves from its position at the center of the sky: “constant as the Northern Star, / Of whose true fixed and resting quality / There is no fellow in the firmament. / [the] one in all [that] doth hold his place” (III.i.60–65). He not only considers himself steadfast but also infallible, beyond the questioning of mortal men, as he compares the foolish idea of him being persuaded of something to the impossible act of hefting the weight of Mount Olympus. In positioning himself thus as a divine figure (the Romans deified certain beloved figures, such as popular leaders, and believed that, upon dying, these figures became ensconced in the firmament), Caesar reveals his belief that he is truly a god. His refusal to pardon Metellus’s banished brother serves to show that his belief in the sanctity of his own authority is unwavering up to the moment that he is killed.