I don't gut a deer anymore personally.
Any "temperature" the guts have in them, won't influence the ham and shoulders much if at all, as they are on the outside of the ribcage.
I know many will start screaming at that, but I have retrieved so many deer the next morning for people over the years, without any "flavor" issues, that I started doing it this way, and now do all my deer.
I lay it on it's side, and cut the legs off at the knees.
I then cape out both legs and body from tail to head from the belly up, and fold the hide up over the back.
I then remove whole shoulder, and whole ham, followed by 1/2 backstrap showing, neckmeat, and whatever flank meat, misc. meat you can pick off.
Then, I fllp the carcass over, and do the same to the other side.
When done correctly, all that is left is a head, spine, and ribcage with organs intact.
Very little mess, except from wound(s).
I bought a used stainless restraunt table for $60, with a sink well built into it. Works great.
I have used a tailgate as well.
Just posting in case someone wants to do a deer this way.