Thought I would share my experience with this issue.
I originally called Apple late last month regarding this issue.
I had it happen AGAIN while they were still open, so I immediately called, I specifically asked the Apple Care Rep to run a diagnostics on the phone before I did anything/answered any questions.
She did as I asked, and confirmed that there wasn't any issues with my phone/battery, and the only thing she could see on the report is the Software wasn't updated/the phone hadn't been backed up. (mind you, the latest Software update had just been released a day or two before I called).
I informed her, that this was on purpose, as I hadn't noticed the issue until I installed the Software version I was currently running (when I called to report the issue).
She of course recommended that I restore the phone to fix the issue. (I was annoyed, as I had Apple Care on the phone, but thought, what the heck, let me update the Software to see if it'll fix the issue.)
Fast forward to about a week after I called. I was on vacation in Vegas (warmer weather), and I noticed I didn't have any issues with it turning off on me.
Got home to WA, and went into the Garage, and bam, even with the newest Software version, it turned off on me.
Weeks go by, then I finally see that Apple is acknowledging the issue, and set up the Battery Repair program.
I contact Apple Via Chat (after hours), and ask them to check if my phone is part of the recall. (call it what you want, it's a recall). After the Rep confirming with their supervisor, I'm told it was part of the recall, and that I would need to go in-store to complete the battery replacement.
I ask if they could do it through the mail. (as I wanted them to forward my phone to to engineering department, so they can actually look into the issue), and was told I would need to contact a Sr advisor in the morning. I also informed the Rep that I wanted a full refund for my Apple Care, as when I originally called, I felt as if Apple tried to blow me off by suggesting I restore the phone as new.
After speaking to a few people, I finally got a Sr Advisor who was able to set up the replacement through the mail, and also get me to someone in Customer Relations to get me a refund on my Apple Care.
Get this, I was also offered an Apple Gift Pack, which included a Hat, Shirt, and Water Bottle. While I accepted the "gift", I did go head with getting a refund for my Apple Care.
My phone and or replacement should be back on Tuesday, so I plan on testing my hot/cold theory to see if the cold makes a difference.