This question has been bothering me for a while and I hope a Christian could give me an answer.

Let's assume that there is a man living deep in a forest with no contact with other humans. Now he is living completely according to the teachings of Jesus, but he does not know that. He even does not know that there is a God.

Would this man go to heaven?

If so, then what if there is another man and he lives among other people and chooses not believe in God or any other belief but still lives completely according to the teachings of Jesus.

Would this man go to heaven?

He would not go to heaven if God leans heavily on the conditions that the man believes (only) in him. But that condition is the one that has nothing to do with how humans interact amongst themselves. So he could be a perfectly good man and an example to other Christians bar the fact that he does not believe in God.

If not, isn't it strange if a man who has done some bad things would still go to heaven because he does believe in God? Why would a being so powerfull as God care so much wether a person believes in him or not?