Ambient operating temperatures for *duino boards
Well, my first guess is that temperature operation would be limited by the oscillator. Now, I'm flying completely by the seat of my pants here, as I haven't looked at the parts on the Arduino. If you pull the specifications on the parts, my guess is that the oscillator is the part with the most limited range. Typically, the bigger the temperature range, the more expensive the oscillator. The other factor that may come into play is the frequency offset. 

As the temperature shifts, the oscillator frequency will shift as well. For a wireless system, this may mean that the transmitter/receiver frequency will shift as well, possibly enough to make the range decrease. 

Dave