As an experienced electric motor repairman here's my two cents worth:
All motors get warm or hot when in use.  The more energy transferred
from one medium to another (electrical-mechanical), the more heat is
generated.  In most cases, the motor is provided with adequate cooling
for the application, most generally by means of a fan built into one
end of the rotating member which draws air in from one end through
vents in the end bell and out the other.  Dave Krall describes this
part of his motor as 'laughable'.

The simple truth is that it's normal for a motor to get hot.  There
isn't any reason to think the motor should not be uncomfortably warm
to the touch.  It is significant that the motor in a player piano is
not in a location where anyone would likely brush against it when in
operation.   Motors in countertop tools and appliances have more active
cooling systems and shields to protect the user.

Perhaps the most noticeable sign of an over-heated motor is the smell
it gives off.  If your motor doesn't smell funny or make strange noises
and the paint isn't turning dark, it's probably just fine.  If you
really want to pay attention to stator temperature I would recommend
either a magnetic surface thermometer or a laser one, they're more
accurate than hand-palms.

Lee Rothrock