You answered your own question.
A man who accepts Christ at his dying hour goes to heaven. For by the grace of Jesus you are saved, but true christians try to be like Christ, hence christian meaning "little christ", so their actions would show their beliefs.
My point is you can't say "oh, I'm going to heaven I got saved as a child" and then lead a sinful life for then one would doubt and I would wonder if you are a christian.
Some believe that if a man accepts Jesus as a young child then denies him as an adult, perhaps becomes atheist then he would still enter the kingdom of God. I'm not too sure if that works.
Works and being saved work hand in hand but by being saved is MORE.
It doesn't matter how many good deeds you do if you trust in Jesus Christ as your savior. But if you do none then you obviously aren't true.
Despite your fallacy this is logical. Be humble, let your actions proclaim your faith, and of course have that faith.
I believe actions show what you believe, but you must speak words also.
*Different meaning of the word work(s).
Side note: I don't have all the answers
PEACE BE WITH YOU
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-chris