Here is my original intent on cooling meat quickly. I have experienced meat related food poisoning by eating antelope that a few of my friends shot and carried around in their pickups for an hour or two in 90 degree weather. Two things they didn't do that I would of done: (1) get that hide off quickly, and (2) get the meat cooled down. Sooner you do that the better the meat is but the main benefit is not improving taste of meat, but in preventing spoilage. Your best quality meat comes if you are able to age the carcass before you process it and remember to remove the glands, fat and that.
However, nothing in my posts says to process the meat immediately. You should never begin butchering until the rigor process is passed. The muscles are going to want to contract and the meat will be tougher than hell if you detach it from the main skeleton. I generally quarter the meat if I don't immediately have a cool place to hang the carcass or a huge cooler like I got now. If the temperature is in the 70s all this is negated and all you really should do is remove the hide and keep it out of the sun and keep insects off the meat.
I got engaged in some sparring on this with nay sayers that dispute the need to cool the meat as "misinformation". That is unfortunate and we don't need to do that here. Some people may be hunting mostly in cool climates and maybe they don't. My antelope hunts are typically in the August to early September time frame and temps are generally still above 80 and sometimes into the 90s still. It all depends on what the weather is.
But because I have been sickened from bad antelope meat that was spoiled, I am pretty religious on skinning, quartering and cooling the meat quickly. I also refuse to accept meat from friends and family if I do not know how they take care of it because of the time of the year it is hunted. Meat related food poisoning can turn deadly quick and I refuse to take that chance. I have been sickened from bad meat four times, specifically antelope. I am not going to take a chance on it being more serious the next time.
If at all possible though, you should keep the carcass whole and put it in a game bag with the skin removed and NOT process the meat until the rigor phase is over and the muscles are relaxed. But sometimes you have to quarter it and put it in the cooler in order to cool it. I got a large cooler that once I remove the front and back hocks the carcass will generally fit nicely and I just keep it cool with frozen bottles of water.
I spoke from my own experience when I started this post and I stick with it. Other's disagree but you know that's OK. They don't have relevance to the way I do things. That does not necessarily make them or me wrong. If they got a method to keep the meat from rotting before it gets processed, that is good enough. Letting meat get or stay warm seriously affects the way it tastes, but that is because of rot or meat that is not correctly processed. Some may not know that because they have done it the way they have for years and never had issues. To me, they are just lucky. I was not lucky and sickened four times from bad antelope, I was shown by a fellow hunter who knew that to remove the hide immediately and get it cooled. Since I have done that, I have never had a gamey tasting antelope and had people eat it and say it can't be antelope. I grew up doing the opposite and carried antelope in the pickup while we tried to fill the other tags. But never again.