Cornell did a study on this and the conclusion was gut it as fast as possible and get the heat as fast as possible.

My butcher told me about this and I bring mine to his cooler immediatley and he has it cut up in about 2 days. I have never had a gamey or tough deer, ever.

On the other hand Europeans wil let game hang for two weeks in warm weather because they claim it tenderizes the meat. I don't know if I would risk that. Those people don't even bathe everyday!