Indifference is neither. So I think that indifference is the opposite of love and hate.
We'll have to agree to disagree on this point then, because going back to the hot/ cold analogy, tepid is not the opposite of hot nor cold. It is in the middle between them. It is neither hot nor cold. Same with indifference. It is neither love nor hate. It is the middle ground between the two. Picture it as two right triangles pointing towards each other with the angle of the hypotenuse indicating the intensity of the emotion. Where the tips touch you have indifference, there the emotions zero out. As you move farther away from indifference you have an increase in that emotion (depending on which way you're moving) until you hit the extreme of that emotion out at the vertical leg of the triangle. Indifference is not the opposite of either emotion. Likewise, the opposite of happy is not ambivalent, it is sad.