It sounds like the output of the op amp is changing as it should.
You should really have a diode across the collector - emitter of the transistor. Usually a 1N4004 will do. Just have the cathode connected to the collector and anode connected to the emitter. This will protect the transistor from inductive voltage spikes from the motor. It doesn't matter what size the motor.
So, my guess is the voltage spike from the motor killed (shorted) the transistor. So, the motor will run all the time and the current is probably too much for the transistor, thus making it hot.
The output from the op amp should also go through a resistor (start with 5kohm) and to the base of the transistor. Otherwise, too much current will flow through the base.
Replace the transistor and add a diode and base resistor as indicated above.
You should really have a diode across the collector - emitter of the transistor. Usually a 1N4004 will do. Just have the cathode connected to the collector and anode connected to the emitter. This will protect the transistor from inductive voltage spikes from the motor. It doesn't matter what size the motor.
So, my guess is the voltage spike from the motor killed (shorted) the transistor. So, the motor will run all the time and the current is probably too much for the transistor, thus making it hot.
The output from the op amp should also go through a resistor (start with 5kohm) and to the base of the transistor. Otherwise, too much current will flow through the base.
Replace the transistor and add a diode and base resistor as indicated above.