3"/Min is way too slow but you don't mention your RPM fastest setting does not tell me anything. Using 18000 RPM 1/16" bit 2 flute bit .002" chip load 72" per minute. This is just an example.
You must have a proper sized chip the chip takes the heat away from the bit if not you will get re-welding of the chips. I cut a fair amount of plastic and if you have it right the chips are warm and the bit can be handled and it is not hot after cutting and I cut dry no coolant.