The use of cold air as a coolant is pretty common when cutting plastics. Typically, you use a device called a "vortex chiller" or "vortex tube" which operates on compressed air. Phenolics aren't usually that difficult to machine, and don't tend to melt themselves onto the cutter like some other plastics, but it couldn't hurt to try. What's probably going on is that "supplier B" is providing cloth-reinforced material, which is really hard to machine, while "A" is giving you the paper-reinforced stuff that works a lot easier.