Who drills thermostats, which drill bit?
 

I replaced thermostat and noticed that old one had small air-passing valve, but new one didn't.
Is that a good idea to drill small hole?

It is a good idea, it only requires a 1/16th" drill bit.

Check the new stat for a air bleed "notch" (yellow circle). Place the notch at the 12 o'clock position like u would a stat with a jiggle valve. If the stat has the notch or jiggle valve, call it good.