Nice catch, Penismith!
The wire must be what distinguishes these cheapo IR heaters from the much more expensive Thermotex ones. Thermotex uses diodes.
So, it looks like we’re back to Wein’s Law. Based on what they’re saying (and assuming it’s true), the carbon fiber must be heated to a sufficient temperature to make it “glow” in far IR.
Since the wristband is neoprene, I suspect it may absorb at least a little IR (like silicone, mentioned above). This makes me wonder whether the heating is primarily due to conduction rather than radiation. Remember that the primary benefit of IR pads is that they use radiation, which actually penetrates into the body.
Still, for the price, I think it’s worth a try. Worse comes to worse, you’ll have a nice wrist warmer :) .