Some dish soap and a wet wash rag will probably work, if you have other funky stuff that won't come off, try some rubbing alcohol on a rag. just stay away from harsh chemicals they can eat through your bow's finish. A prime example would be insect repellant, it's innocent enough, it's summer, your shooting but mosquitos are buzzing you so you put some insect spray on and then pick up your bow and continue shooting, then you notice the grip area and how the finish has been removed.
You can leave your bow in the car when it's cold, just don't leave it strung up if the weather is hot or the bow will delaminate.