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It sounds like your iPhone is not behaving correctly. The steps in this article can help with troubleshooting the battery issue you're seeing:
iPhone and iPod touch: Charging the battery
iPhone or iPod touch displays the low-battery image and is unresponsive
If you see the image below, charge the iPhone or iPod touch with USB power adapter for at least 15 minutes.
You should see this image when iPhone or iPod touch begins to charge:
If the screen still displays the low-battery icon, try turning the iPhone or iPod touch off and then on again.
If the issue persists, follow these troubleshooting steps.
Sorry to say, but your feedback is pathetic! Are you impling that I don't know how to charge my phone? Well, I though I was clear, the problem is that the phone doesn't like cold weather, even mild weather by Canadian standards. Like 10 Celsius and it shuts down and give the battery sign. Again, even with the battery fully charged. Crap hardware for such a good system!
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I just took mine into Genius Bar and they advised me that there was nothing they can do and it's just the cold weather. I told them that it happens even though I've been indoors the whole time. They did a diagnostic and found out that my battery is pretty much close to DEAD and I have to pay to replace it for $80. Takes 1 hour...
I've had my iPhone for a total of 1 year and 3 months.
I have this same problem - full charge but when temperature gets cold (below 0 F), the phone just shuts off and behaves as if battery is dead. When it is charged for a bit it wakes up at something less than original battery life (before it died) but waaay more than the 0-10 % you might expect.
My solution has been an external Lithium Ion battery pack. It is about the same size as 4S but twice as thick. It has a 2.1 Amp USB port for the charging cable. Plug the phone in with charging cable and use it while leaving it plugged in. Its a little bulky but better than nothing at all. Side note: At -30 F the charging cable gets really stiff. At about -30F I could unplug this external batter pack, count to 5, and the phone would die. Sometimes the phone would wake up if I plugged it back in......sometimes the phone had to be warmed up to wake it back up. The external battery pack has enough mass that it won't get too cold when in outside pockets of jacket in -30 deg F for 2 or 3 hours. Any longer than that the lithium ion battery pack gets too cold and will die as well, just like the battery in the phone. By then I'm cold anyway and time to get off the snowmobile and warm up.
Sadly I have had the same pathetic experience going back to the first year I got mine. 10 celcius with 75% charge and it would go black just from leaving my house to the car. They tested the battery back in that first year under warranty and said it was fine, also saying "cellphones don't work well in the cold". What a pile of crap. I'm not in Antarctica. A year later (without warranty) retested and was told it was bad and I should pay to replace it. Scam. I found out the problem is with the phone itself, and I have a very hard time believing Apple doesn't know it. Here's how I know: I resorted to trying an aftermarket battery a month ago. When tested by the nearest Apple Store they said my battery tested strong, but all the same problems keep happening ...
In addition, my 4s was failing "from being too cold" when everyone else's phones were still working just fine. We all walk the same walk from the parking lot, and colleagues with blackberry, LG, samsung, and even other iPhone models are just fine when mine was failing. In fact no matter how cold it got, even minus temperatures, no one else's phone died. Only my 4s ... Apple makes a sh-t model and doesn't do what's right for the customer. Not cool Apple