I havent had to cut a whole lot of animals in the bush, but ive done a fair number and have yet to loose any meat. But, I havent had to do it in extremely warm environments yet.
I think the biggest mistake guys make is not getting the meat cooled to ambient temp as soon as possible. Decomposition starts at the moment of death (I knew meat science classes would come in handy someday).
I bone everything, and will even break large quarters (especially on something the size of an Elk) down into the muscle groups. I carry a small 4'x4' piece of tyvek (multiple uses) with me and lay the meat out on that in the shade if possible. Even if its still 90 degrees out, thats better than 100+ degrees. Get as much fat and tallow off as you can, and remove blood as best you can. Those chunks of coagulated blood hold a lot of moisture. These smaller chunks cool a LOT faster. If your game bags are big and full, its a good idea to spread that meat out again in the early, coldest part of the morning to further chill back down. Good, tight knit bags help for flies. Those cheap cheese cloth ones dont. Airflow helps too. Develop that crust, dry out the surface.
If your nighttime temps are dropping to 50 or below (which is pretty common in the North during September) and you hang in a smart place during the day, youd be surprised how long meat will keep, even if daytime temps are hot.
We kept an elk for 7 days once (some lucky SOB tagged out the first day) without ice in this manner with daytime temps averaging mid 70's but with cool nights.
Lost an antelope cape once though. Darn thing was in the deep freeze within 6 hours of dyeing. The other one (killed eariler even), was just fine. Riddle me that.