Brand new iPhone 5 overheating and shutting off

Hey! My name is Cory and on the 8th I got a new iPhone 5 from the Verizon store by my house. I love it! But since day 1 I've had issues with the phone getting very hot and shutting itself off (it will give me a message "iPhone needs to cool down before you can use it"), this happens maybe 4 times a day, I've been meaning to go to Verizon (apple store is far), but I'm a busy man working 2 jobs... So my question is, if I'm still within the 2 weeks window can I just take my phone in and have it exchanged for a new one? The recipe got wet (I love in portland!) so I no longer have it, should I bring the box and all the accessories or just the phone? Will this be a smooth processes or should I be worried about getting stuck with this phone?