As long as you don't have the deer laying on the hot hood of a vehicle you are normally OK - unless of course its 80 degrees out all day!

In any case, I'd put a small stick inside the chest cavity to keep the air circulating to cool the deer down. it is is overly warm out you can even pack ice inside the carcass - but thats pretty extreme. Let the air get to the deer when traveling home. Black pepper can be sprinkled into the cavity as well if flies are an issue.