Honestly I am new to hunting down here since I had to have a major surgery right after moving here where my wife is from, but up north we always hung deer in the garage overnight and it was very cold out. If I was having to wait on processing a deer in 50 degree weather, I would fill the cavity with ice and pour ice over the whole body. Quarter it, throw it in some large coolers or storage bins doubled up (if you don’t have enough coolers) and put it out of the sun. That will keep the deer nice and fresh for you. They also make coolers for game animals that I found when looking in to it. Also you can get those really long white IGLOO coolers for dirt cheap money if you go to their company off the Katy Freeway. They have a small store on the side of the company building where they sell coolers with small blems like color splotches on them, but they work completely fine and are really discounted in price. Hope this helps you out.
I really like these and want to get one but they are kind of expensive. Made in Oklahoma.
https://www.bowhunting.com/blog/2009/03/31/your-game-wont-spoil-with-a-trophy-bag-game-kooler/