S3 Continuously shuts down?

My galaxy s3 has been acting up. What I mean by this is that it shuts itself completely off at random points. This problem began after I overheated it several times using an app. I thought that it was a software issue at first, but I attempted a factory reset and it still does not let me get through the setup wizard.
With this, i have 2 questions. One, is this covered under a warranty, and 2, is there anyone who has a solution for this, or should I go to my carrier to try to get a replacement?

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