For a three hour time period, you really don't need to do anything other than keep the bird as clean as you can and minimize damage to the feathers.
Most of the damage done to a bird is from the shot and the bird flopping around afterward. If you plan on mounting your bird, try to shoot it in the head only. With today's emphasis on tight chokes and shot concentration, a gobbler shot in the upper neck area below the head is often going to have considerable feather damage. That is very difficult to repair.
Heads can be replaced easily, but if you want a mount that is totally comprised of your own turkey, head and all, then leave the shotgun/choke that will take a gobber's head off at twenty yards at home.
After shooting your bird, try to minimize feather loss and breakage by subduing a flopping bird as carefully and gently as possible. That is easier said than done, but the more a gobbler flops around on the ground, the more feathers are dislodged or broken. Although it can be punishing for you, one of the best ways to minimize feather loss and damage is to get to the bird quickly after the shot and if it is flopping (or starts at some point), grab it by the legs and hold it up at arms length and hold on for dear life until it stops. One thing to remember is that if a dead gobbler is not flopping, do not try to pick it up for a while because doing so will often trigger wild flopping by a bird that is otherwise motionless.
If a lot of feathers are dislodged from the bird after the shot, you can gather them up if you want to take the time and take them with you. However, most taxidermists will have a supply of replacement feathers in their shops for those instances where they need to replace feathers on a cape.
When transporting your bird, do whatever it takes to keep from damaging the cape. Blood is less of an issue than most people think. In the mounting process, the cape is thoroughly washed and cleaned anyway, so blood will be washed out of the cape. However, it is a good idea to try to minimize the amount of blood (and other debris/contaminants) that can get on the cape.
The rest is common sense. Just try to treat the bird gently between kill and delivery. Keep the feathers from bending, breaking, or coming loose as much as possible.
And finally, it takes a lot of mistreatment between kill and taxidermist for a gobbler to not be mountable. If you kill a bird that you feel is a "mounter", but you think may have been damaged beyond saving, don't just give up the idea. A competent taxidermist that wants to make the effort can salvage a decent mount out of all but the most damaged birds.
The notable exception to that, however, is when the skin has "spoiled" (started to decompose). That process takes quite a bit longer than three hours though,...even in the harshest of conditions.
