I want to see my boyfriends text messages
What do you think that you will get from looking at his messages?
I think that I'll be able to stop caring about her, if I see that she is gone
I think that that is an invasion of privacy. If you are so worried about what he is saying to her, you should just ask him about his feeling towards her.
Well, I never hear him talk about her
It's likely that your boyfriend has moved on from his old relationships, and if you have no reason to doubt this, you should respect his privacy.  If you are really worried, you can let him know how you feel, but sneaking into his private correspondence is always wrong.