Using thermal overload protection in AC-DC PWM motor driver circut
That motor-protection is protecting the complete circuit - transformer, rectifier, PWM modulator and motor.

Your motor is rated at 12 V, 3 A. From the equation \$ P = VI \$ we can calculate that it is a 36 W motor.

Discounting losses for a moment we can calculate the required current at 230 V AC to provide 36 W. Using the same formula and rearranging we get \$ I = \frac {P}{V} = \frac {36}{230} = 0.16~A \$.

Allowing for some losses in the transformer, wiring and PWM (in)efficiency I would probably set the trip current to 200 mA. The protection device looks like the right choice.