Originally Posted by Zexious
^If she purchased the phone through Best Buy, she may have the warranty through them and not through Apple. I'm not sure how warranties work... just toss'n that out there~
Apple doesn't care where you bought their product, they WILL support it. Their customer service is second to none. However, warranty is 1 year on iPhones, so it's probably fruitless unless the OP bought an extended warranty. Worth going to an Apple store anyways as you may be surprised - go with a good attitude and ask for guidance - I've had out of warranty stuff replaced at our local Apple store before simply out of goodwill. Attitude is key.
Now, that all said, these sorts of things can sometimes happen as a result of corruption issues - OP, try doing a "Factory reset" (A FULL reset, not just a partial), then RESTORE the phone in iTunes, and then set it up again as a NEW PHONE. In other words, don't restore from a backup.
Sometimes this will solve oddities like this.
Our iPhones all experience the super-cold shutdown problem though - although that will happen on most phones - the cold just saps the life out of the battery. Try keeping it in an inside pocket of your jacket.