for animals as small as deer, I think that aging is overrated. What is far, far, far more important is how you dress the animal in the field. Get the guts out ASAP - before you move the carcass! Then hang it and take off the hide as soon as you possibly can. If 20C is the coolest you can manage, I'd be thinking about butchering the carcass within 2 or 3 days at most. The meat itself actually lasts a while at these temps: if kept *dry* the surface will dry and harden, and keep most of the insects out. I don't think it's spoilage that you need to be most concerned about, but the fact that the texture will start to suffer, and you'll end up with mushy grey steaks
I've butchered and packaged meat before it even went into rigor - it was just fine, although the cuts looked a little funny after frozen and then thawed - jagged surfaces, like it was cut up with a chainsaw. Otherwise they were fine