The results weren't promising, at least with a plastic barrel. The barrel is from the Meng Leopard C2 Mexas. This barrel already has a protective heat shield on it, but it's all I had handy. Sorry for the out of focus pictures
Standard heat shrink tubing that fits snugly over the barrel:

I used a hair dryer to heat the shrink tubing. It shrank, but I stopped it when I felt that the barrel was getting hot enough to start deforming:

I sliced it open and the inside of the tubing had copied some of the details of the barrel, so that was encouraging.
Next, I tried some heat shrink tape. I wrapped it lengthwise along the barrel. The tape is slightly self sticking and is designed to wrap tightly around pipes or wires, but it was difficult to wrap the tape in this orientation. Even cold it showed some details from the barrel, but it had the same problem as with Polyolefin heatshrink tubing.
Wrapped as tight as tight as I could get it:

After heating:

The technique may work on metal barrels. I may have one that I can try this on; I'll look for it tomorrow. For plastic barrels, I think something like Tamiya tape would work OK.