Do carbon alt-bars exist?

Looking to switchup from the stock bars on my beloved Surly Big Fat Dummy. I'm particularly intrigued by the Jones Loop or Surly Molokos but here's the catch- I want carbon fiber bars. Even through poagies, my hands get cold on longer rides (Raynauds syndrome, yay). Especially when I leave my bike parked on longer grocery missions, the bars sap my heat and will to ride!

Carbon bars supposedly conduct less heat… Are there any carbon (or other?) alt-bars out there that will better preserve heat while giving me some summertime grip options? Do I go full psycho with a seasonal bar swap? Any other ways the cold-blooded can stay warm through an Alaskan winter season?

Pics in both seasonal modes for bike tax.