This year we experienced the same weather on our elk hunt.

In the past I was big on skinning right away until one year, on a 66 degree day I shot a nice sized bull elk. We were well over a mile away from the nearest road and worse we were downhill so the hike back was pretty steep uphill effectively multplying the perceived distance. We employed the gutless method and skinned the quarters although we did leave bone in the quarters but there was lots of meat like the backstrap with no bone in them. We hung the meat for the night and temps dropped down into the 30's. The next day we rounded up some friends and went back and hauled out the elk and took us most of the day. By the time we got the elk back to the cooler to hang and process the meat hadn't spoiled but it got this tough layer on the meat. I had a lot of meat wasted because of this 1/4 to 1/2 thick layer of almost jerky'd like meat all the way around. Underneath that it was fine. (I process my own so I notice these things) Nearly every steak and roast had to be trimmed quite a bit of this hardened meat.

Since then I half or quarter the animals but I don't skin it until I have the animal in the cooler to hang or just before I get it in there. I have found the skin actually preserves the meat under it. I think the important part is to get a bag on it, get it in the shade, and hung to cool off.

This year we halved two elk, bagged them, and hung them in a shady tree for 3 days and we didn't skin them until we got them home and ready to hang in the cooler for a few days. They did great and we had very little loss of meat, maybe 10lbs. at best. 30's at night, 60's during the day. BTW they are some of the best tasting elk I've had in a while too.