I vote for it does not matter. Nobody runs a drill press for five
minutes anyway.

Your motor should have a temperature rise in celsius stamped on the
nameplate, or alternatively insulation class. If you post this info,
or the whole nameplate, someone here could tell you whether the
observed temperature rise is justified. Many modern motors are
designed to run relatively hot.

You can get a perfectly quantified answer to your question if you
post nameplate data.

i