The cold weather keeps deer moving during the day, which makes it likely you will see them and perhaps have a shot. If it is warm, most of the deer movement will occur under the cover of darkness, when it is cooler. The only effect temps have on the rut is when you will actually see deer movement. With thier winter fur, the deer are more comfortable to move when it's not 70 degrees F and sunny like it is here in VA right now.
I may be wrong, but I havn't seen any deer on my stands since I shot one on Oct. 30th. The weather has been too warm and that is just what I believe, others may differ, but I sat out today because of the high temp and near full moon. I look for all of next week to be very good because of the moon phase and expected lower temps, but that's just me