To go for the second question first –
2/ How easily does the pro spin, with and without the motor connected? A hot motor is one that is working hard, either because its turning an unsuitable prop and/or running on the wrong voltage and/or there is friction in the shaft that it has to overcome.
Is the TX known to work OK with anything else?
1/ Although there is no interference, an overworked motor can produce its own, and reduce the effectiveness of the signal, either by generating radio frequency that the aerial picks up, or by injecting the signal into the power lines.