Exactly.
Meat-science studies have shown that meat under the hide is essentially sterile. As soon as you pull the hide off, you open up the surface to air-borne bacteria. Therefore the logical thing to do, even in warm weather, is to expose as little of the meat surface to air as possible--unless, of course, you have access to a walk-in cooler or something similar.
Another thing that can be done on smaller animals (deer, antelope, etc.) in warm weather is place as many bags of ice inside the body cavity as possible. This cools things down right away. On an early-season sheep hunt I have also put the quarters inside plastic bags and placed them in a cold creek.
