iPod Nano battery loses charge when it's cold
The temperature you describe is not cold enough to affect battery functions too much. It’s within the operating temperatures and it shouldn’t happen. Take a look at the temperature charts in the Apple iPod Battery page and if it doesn’t perform as expected, contact them immediately.

UPDATE: If the iPod is not under warranty, you’re pretty much “hosed”, however, you can attempt a manual battery replacement. This google query is a good starting point.