Just bought my MBP-R 13'' last week, it lives on a well ventilated desk in my room and when it's not there it's in a well ventilated, air conditioned classroom.
This morning I went to power it up to take notes in one of my classes, it wouldn't turn on. Putting it away in my backpack I continued on my day. A short while later I feel an intense heat radiating through my backpack, I take out the laptop, it is too hot to touch, literally. Despite the proactive measures I take to keep this laptop in top condition it is now overheated, will not turn on, it is and still hot as I write this from an Apple Store laptop, hours later! The fan was working as hard as it could but it's not running anymore. Odd.
Unfortunately I have no idea why this situation happened. I use this computer for web browsing, documents, and occasionally iTunes / Spotify. No intensive tasks. Is this a software issue? A hardware issue? Currently at the Apple store, I'm hoping they will replace the laptop completely. The concern I have is that the heat will have caused long term thermal damage to the internal components of the computer.