Larry Norman's suggestion of comparing the temperature of various
motors under various load conditions is a good one.  A couple of
additional points --

A safe temperature for one motor might not be safe for another one,
so a conservative safe temperature should be used so as to not inspire
false confidence of safety.  Aeolian used at least three different
motors and they may differ in their safe operating temperatures.

Defects in the motor will also lower the safe operating temperature.
A motor with damaged wiring may get hotter in spots that are not easy
to measure.  A motor that was over-oiled may behave differently.

Non-contact infrared thermometers are readily available and quite
inexpensive today.  I use them for all purposes including the
measurement of motor temperature in various places.  You can easily
measure the temperature of the coils without danger of sticking a
glass thermometer into a running motor.  Also, it is difficult to get
accurate temperature measurements from surfaces without the right kind
of thermometer.

I am away from home and can not measure the temperature of my various
motors or I would give some numbers that I consider safe.

If a piano is to be used for short periods only, almost any motor that
does not make terrible noise or smell like it is burning up is probably
okay.  Using an old motor for an extended period of time requires being
very sure about its safety.

I really prefer to rewind motors or replace them with modern ones that
have thermal protection, or add a thermal protection device and set the
cutoff temperature at a very conservative level.  If you locate the
pump remotely, you can use a modern ugly and noisier motor that is
safer.  I have several different thermo switches but I forget what
temperature ratings they have.  I can check when I am home again.

I did fairly extensive testing running different motors wound with
cotton covered wire under various loads, measuring the temperature,
etc., and choosing a cutoff switch that worked when strapped to the
motor case but did not allow the windings or rotor to get too hot.
I just don't remember well enough what I decided on and don't want
to guess.

If you are concerned more with overheating the soundboard than safety
because the motor was rewound with wire that will not fail, you can
provide a shield and maybe modify the belly cloth to allow more
airflow.  The remote pump is the ideal situation if this is your
concern.

Best regards,
Spencer Chase