Regarding protective devices for electric motors: nothing will protect
against the starting winding being energized for any longer than it
takes the motor to come up to speed.  A start winding is wound with
small-gauge wire in order to get enough turns into the given space, and
cannot carry current for more than a few seconds before it overheats.
No thermal device can react that fast even if it were attached right
next to the winding.  (There are thermal relays that can, but those are
wired in series with the winding and are sized for the motor's starting
current.  They don't detect the temperature of the motor).

I used to rewind motors in a small shop, in summers between my college
years.  I would guess that ten seconds of energizing is enough to smoke
the insulation on a start winding and char the insulation, and much
longer would raise the wire temperature to a red heat, easily enough to
ignite enamel insulation and the organic varnish used to keep the wires
in place.  In our rewinds we used glass-insulated wire for the start
winding that actually would withstand red heat, but I'm sure no piano
motor ever used that.

Alan Douglas