Your absolutly right Paul. The first few hours are extremely important in reducing the remnants of the animals body heat.
If the animal was killed on an evening hunt, and you know the temp will fall at night, no worries, but for morning kills, you could run into problems, especially you southern boys.
One thing you can do (if you have the means) is to gut and immediatly flush out the chest cavity with lots of cold water. Cold water really saps alot of that body heat out of the carcass.
If you have a bad hit (paunch and guts) you should be washing them out anyway. I also always wash any liver blood out, if I hit the liver, they get treated just like a gutshot. Luckily, Ive only had to suffer through one gutshot animal in my hunting career.
Once you get the body heat dissipated youll be amazed what that carcass can sit through with no ill-effects.
On a side note, I had some buddies that went out antelope hunting, it was early september, daytime temps in the upper 70's. They hunted for four days, had two goats in the back of the suburban for three of those days in that heat (idiots never took em out). By the time they came home, those goats STUNK! Not bad, but you could tell.
But they claim it was the best goat they ever had. I just had to take their word for it.
Boone