66 Barracuda Blower Motor Resistor

Is the fan running while the resistor is smoking? Is the resistor in the fan airflow? You could have some debris in the housing blocking air flow to the resistor. They will over heat if they don’t have good airflow through them.

Check the current on the motor. Sounds like it is pulling too much. Some dc motors will run with partially shorted coils, they will just pull a lot of current.

If you unplug the fan, does the resistor still smoke? That could mean a short somewhere else in the circuit.

Just some things to try....