LEAVE the innards in for a day or so!?! Sounds like a good way to have your animals meat go sour (Rotten!)
Gut animal as soon as your find it (do make sure that it is dead, first), or bone it out, ASAP. You want the meat to cool as fast as possible, to prevent spoilage.
Some people who quarter their game leave the hide on to "protect the meat from dirt/leaves, etc." IMOHO, the hide should be removed as soon as possible. Two reasons, one to let the meat cool, and two, the hide is MUCH easier to remove from a freshly killed animal. I carry cheese cloth bags to cover my quarters/boned out meat, to protect it from flies, hornets, and dirt.