I don’t really know what I’m talking about, but could the cage be ‘baffling’ the airflow in some way? Is that a thing? And/or, something to do with ‘resonance’ or simple harmonic motion (and with that, I’m definitely way out of my depth).
Is the cage squished or otherwise misshapen? Does the motor settle down to a certain non-design speed (or maybe not reach its design speed) from ‘cold’, but then, when you turn it off and back on when ‘warm’, it can ‘rev through’ that ‘sticking point’ and reach the proper fully effective speed?
JFC. Leave it, Wza.