We used to use one that you put a gel-pack in the microwave (Pyro Flight). I don't think they make them anymore and you had to time it out right. It wasn't easy to find a microwave at the fields after it went cold.
A newer electric one that works really well is the Bat Cozy.
Yes, Carbon Composite bats are more brittle and likely to break in the cold. The cold (below 60 degree F) makes the balls more dense and the carbon fibers of the bat more rigid/less flexible. Both factors work against the bats.
A bat warmer that actually heats the barrel (not just insulate...