VERY warm weather shifts more of deer activity to the cooler, night-time hours. Deer are loading their body with fats right now, and that produces a thick layer of outer fat that is like us wearing a puffy down jacket. If you have to run around chasing females wearing a down jacket, when are you going to do it? During the heat of the day or at night when it's cooler? And deer don't have the temperature regulation system we do (sweating).
But heat does not shift the dates of breeding. Breeding will occur on about the same dates each year, with a few rare exceptions. The heat just shifts more of the chasing to the night-time hours.
diamond hunter, in your area, you should see the rut at the normal time of year. However, those in West TN and western Middle TN may not. One of the factors that can delay the rut is poor health or even stressed health. West of Nashville, the summer and fall heat and drought, and resulting acorn failure, have the deer quite physically stressed. When deer are physically stressed, breeding timing can be delayed. In addition, breed "rituals" such as rubbing and scraping, can be VERY muted. The bucks simply don't have the extra energy required to go through these ritual motions.
The worst situation like this I've ever seen was in 2007. That year we had a severe late freeze that not only killed all the summer forbs deer rely on, but also wiped out the following falls acorn crop. That summer was record heat and drought. By fall, the environment was burned to a crisp. In addition, we experienced the worst EHD outbreak in recent memory in Middle and West TN, with some areas losing 30-50% of the deer population. The fall of 2007 was lowest amount of rubbing and scraping I've recorded in 35 years, and peak breeding appeared to be delayed approximately 3 weeks.
Now the conditions are not as severe this year as they were in 2007 (no EHD outbreak), but I still suspect the areas affected the worst by the drought will see a delayed and muted rut.