I have a Kindle II and it worked normally into the 40's but started getting sluggish as it got down into the mid-30's. Right around freezing point, it got "confused" and then, eventually, I got the dreaded totally BLANK screen. Froze there and wouldn't do anything else after that.
When I got home, I did a little research online and read about trying a hard reset by holding the sliding switch in the 'on' position for something like a minute. Tried it and, voila!, it came right back. Everything was intact, including my downloaded books.