I’ve been trying to get a system like that ^ working on the msr windburner, which doesn’t have a gap through which you can feed the flattened copper tube into the flame. The best I’ve tried so far is using a few “slats” made from many layers of aluminum foil attached to the outside of the burner with a hose clamp, and squeezed against the gas cannister with rubber bands. The heat transfer seems to be about right, and you can adjust for different temperatures by changing the number of slats. I at least prefer it to the warm-water-in-the-cap method (since if the water is too warm you get a conflagration in your tent, and you also end up with ice on the cannister and cap, which eventually finds its way onto your down clothing) or the swapping-cannisters-into-jacket method (since you need an extra cannister, and swapping takes time).
The downsides to this method are that carrying a dime to work the hose clamp, and twisting the hose clamp, are somewhat annoying. Plus the hose clamp is an awkwardly shaped, sharp thing, so it’s hard to pack in a way that doesn’t damage delicate clothing and inflatable pads.
