I'm using the Time.h library I found here:
http://www.arduino.cc/playground/Code/time
The included sample, TimeRTCSet, has the method I used to set it.
As far as ambient air temps go my Arduino has spent most of it's running time around 20C or lower. The last week has been closer to 15C. It's in an unheated shop.
Time.h includes a DS1307RTC.h, I notice you aren't using Time.h