If it looks like it is melting, pull out drill, then stop, and wait for things to cool.
Water does help cool things, but not critical.
Do not push hard. It can shatter a bit as it comes through.
It sometimes works better to drill half way from each side, but if you do not drill straight,
it may not like up quite right.
If you are near Union City, I have quite a few different size hole saws.