If you have looked through our FAQ's you may have seen in my answers for this type of situation that the most critical elements are time and temperature. The longer the bacteria is exposed to temperatures above 40F the faster it will multiple.
In the case of a gut shot deer the bacteria in the stomach, along with the stomach acids, digested foods, fecal material, etc are given a greater exposure to the surrounding muscles that are used by the hunter.
In the case of your deer, assuming you mean 2:30 p.m. the next afternoon, the deer spent 20 &1/2 hours before being field dressed. At the temperatures you describe we can assume that the internal cavity of the deer remained above 40Fand most likely above 50F the entire time.
At about this time last year, at slightly cooler temperatures than you had, a deer was hit by a car by my neighbors at 11p.m.
I received a call at 7:00 a.m and I went over and field dressed. I rinsed it and dusted the inside heavily with baking soda and had it in the cooler by 7:30a.m. I too noticed an odor when field dressing it but figured it would be confined to the stomach cavity.
I cut it up the next day and froze it immediately. The problem became evident when we went to prepare it, as soon as you started to cook it, the gases trapped in the cells of the meat were released and the smell was very evident. When eating it, it seemed like you could "taste" the smell. The amazing part was this was the burger that was made with pork and beef added to the venison! We dumped the whole works.
As far as your deer, my guess is that you will find out if there's a problem when you cook it. Because we all have individual tastes and expectations when it comes to the food we eat, it all boils down to the fact that you have to be the judge. As far as my opinion, I believe you may be pushing the limits.

Good luck,
Dave