I think you will be just fine. I believe most of the posts are a good way to handle meat. But in back country hunting ice, coolers, etc are not often available. A lot of animals are killed on 60 degree temps and kept for 5-7 days. When I kill an animal it hangs in my garage with the his hide on for 5-7 days and sometimes the day time temp is above 50. Meat holds temp very well and if you cooled it down that night and put a blanket on it it will be perfect. (Great thing to do by the way with the blanket. I have twice killed deer on 80 degree temps and cooled them in a creek then stuffed into my sleeping bag to stay cool).
Process the deer, you will know if its bad. But I'm strongly guessing you are all good.