I have always used the bags of ice and wrapped them in a tarp. I also make sure that any water from the melting ice either stays in the bag or drains away quickly. I have never really noticed the difference between a deer hung for a few day or one cut the day it was dropped anyway.
When the weather is really warm I walk to my stand naked. Less chance of breaking a sweat and other hunters who may see you vacate the area pretty quickly.