As others have pointed out, in the warm early season weather you posited in your initial post, the number 1 priority is to get the meat cool. Bacteria is present in all animals -- including human beings -- but active immune systems keep them in check. After the animal dies, however, the immune system stops functioning and the bacteria can reproduce rapidly. The higher the temperature, the more rapidly bacteria reproduce.

Large muscles around a big bone are supposed to stay warm longest and be most susceptible to souring due to heat. Don't gut. Take the animal apart from the outside, as it were, as folks have described above. You can lay meat on cool rocks which may help to conduct heat away from the meat, but keep the meat clean. After you have the animal quartered, deboning is an additional step that can help cool the meat quickly. If you are going to pack the meat on your own back, of course, deboning makes even more sense.

Have more than one appropriate knife, because knives break. Have sharp knives. You may wish to take a sharpener. It sounds like there is some disagreement on this, but it seems to me to make sense to have a saw. I guess if you aren't going to saw off the ribs and take the ribs with you, you might be able to live without a saw. A good thing about the afore mentioned Wyoming saw is that it comes with both a meat/bone blade and a wood blade, so the saw can do double duty. This saw also takes down and forms a pretty compact, lightweight package.

I also advise you to get some practice on other meat -- butchering and deboning deer, for example -- if you don't already have this experience. You can also debone leg of lamb, which is something you can do outside of deer season.