Several years ago I had a total joint replacement done to my left shoulder. For several weeks after I had to keep my shoulder iced down. I used a small machine that has a small ice cooler connected to a fan that pumps cold air through an insulated hose to a dispersing plate that distributes the air to the area needing cooling. Immediately I thought, "barrel chiller!" Thanks to my insurance company for paying for it I decided to repurpose it for cooling down my barrels. Although it had a 110AC plug the fan is identical to a computer cooling fan that runs on 5V so I rewired it and connected it to a trail camera 6V battery pack. Then I cut off the end of a plastic funnel and attached it to the end of the hose so it would fit inside the action pointing down the chamber of my rifles. It would be relatively easy to make one by putting a fan inside of a plastic box with a nipple on each end to attach the hoses and drilling a hole through a small cooler to run one hose through.
This thing, once filled with ice, will cool a barrel in a few minutes.