Yes, LeBron James will stay with the Miami Heat, because he has a great deal with the Miami Heat. He has a lot of endorsement deals, and he has been very successful with the Heat. Who would want to leave the place where you are a star? He is too popular there to leave now.
LeBron James wants to win championships. Before he went to Miami, he had made the finals once in 7 seasons. In Miami, his squad made it all 4 years, netting him 2 championship rings. Pat Riley is going to "retool" the roster, as he put it, so I'm sure their will be added talent to compliment LeBron. Now, if Riley fails to make any moves to improve the roster, LeBron could decide to leave for greener pastures.
He already requested to be a free agent and I think he will go with whoever gives him the most money. He doesn't seem like a very loyal player. He already left Cleveland and many people were shocked, but knowing his history now I don't think anyone should be surprised if he decides to leave Miami.
I think that Lebron James has no loyalty and will go where the most money is. I think it is going to come down a biding war and he is going to go where he can bank the most cash. He will go where he can get the most and not worry as much about being a contender.