Just to give a recent example, a few of us went into the woods last weekend during NH bow season. My buddy shot and tagged a nice doe. Even though we usually butcher our deer, my buddy decided to drop off his doe to have butchered. Between the time he tagged it, dressed it out and dragged it to the tuck, it was a few hours old. He then took it to the butcher, about an hour away, who said his deer was fine. His deer was ready to pick up two days later. The entire time, the temp was about 75 degrees.
You should have no problem...dress it out and get it to the processor as soon as you can. Pot some ice in the cavity and you should be fine.
Good Luck!