Does i shut down because of heat or low battery or what? If you have to keep it plugged in, sounds like a battery issue. Does it have a replaceable battery? Do you have extended warranty? If so, this can be used for a free replacement via Verizon.
No, it is not hot or cold. It does not have access to battery and no extended warranty. Could it be a software issue? It stays off until battery runs out even if you put it on a charger. Then it turns itself back on. Possibly possessed?!?