You could always do the old tile-cutting trick. Use the saw to cut a sponge. Now you have a sponge that perfectly fits inside the hole saw. Get it wet, and leave it in the saw when you cut. Now your hole saw will be cooled by the water in the sponge.

It’s an old trick for when you can’t easily keep running water on a tile saw while cutting a hole. Cuz you typically cut tile under water to prevent your blade from heating up. But if that’s not feasible, you can essentially just fill your saw blade with water instead.

You can fix the warping, or close-enough to "fixed", if you're poor or cheap or just obsessed with wringing the value from each purchase ( hi ).

Luckilly, the line between "fixable" and "holy shit, this things wobbling so much its going to grab, walk its way off the board, and cut into my leg" is readilly apparent, to anyone who has any business using such tools.