I have very little practical experience with Carbon barrels. I do have a fair bit in other applications. I have looked at them numerous times but can't get past the reservations and have always ended up with a steel barrel with varying contours or maybe fluting to save weight.
That said, Carbon Fiber itself is as good or likely better heat transfer than Stainless - that's fibers only. However when laid up in an epoxy it's much worse. When I've spoken with manufacturers they are quick to quote the bare carbon properties but skip over the assembly. It would be possible to get better with a more complex laminate including copper or silver, etc. but to my knowledge none of the barrels have that. BTW, SS is worse heat transfer (better insulator) than non-stainless by a bit. That's talking generalities and specific materials, alloys and techniques will vary.
LB for LB Carbon Fiber has the potential to be much stiffer than steel. Whether that translates over in the real world I'm still sceptical. And add in the thermal properties and different materials moving against each other we'll see...
Thanks for posting up the test results, it's great information.