I start worrying about temperature on two counts:

(1) Is it warm enough for the blow flies? Blow fly eggs can gestate from eggs to maggots (larvae) in 24 hours in continued warm/moist conditions. You have to get it cooled at some point (soon, perhaps night air) to cause the fly eggs to go dormant and and stop the "development clock". Fortunately the same warm weather that allows the flies to be abundant also cause the meat to "rind up" which acts as a natural barrier to maggots.

(2) Daytime high temperatures over 75 degrees (pretty easy in early seasons) which even after a cool night can lead to "green meat". Even in small patches this stuff is problematic. Once you smell it, it becomes difficult to discern the good meat from the bad.

So skin the quarters, bag them, get them into the shade (conifers are my favorite --- on a north slope even better but that depends on where you bagged your critter), when you hang them don't let them touch each other. Get them to camp ASAP, horses shine on this latter one, we hauled out 6 elk in one day from 4 to 5 miles back in.

If the weather was warmish and I was NOT butchering in camp, then I would be making the trip to town to the local processor and have him butcher it. Since we go for "gourmet elk" I wouldn't haul quarters long distance on the way home unless I could keep them cold and away from the windstream.

BTW, you can process in camp without freezers, just use coolers and dry ice. It will take 1 pound of dry ice to sharp freeze 2 pounds of packaged elk in warm weather. Note if overnight temperatures drop to 10 to 15 degrees it will sharp freeze over night just by "setting it out". At 19 to 22 degrees you are screwed, it is not enough, even though it is sub-freezing it will "slush" but not sharp freeze. If you have an empty pickup bed, then lay the packages (not touching) in the pickup bed and the steel will help transfer the cold of the night air to the meat.

EKM