Let me jabber on a little about the motor and see if I can explain it's workings a little more.
If you take just the motor (without a fan for the sake of discussusion) and the battery in a circuit, when you connect the motor, it will accelerate to a particular speed and then stay at that speed. The amps will be at some fairly low level without a load on the motor. It is the 'back voltage' generated by the motor turning that determines the speed at which the motor runs and the amount of current flowing in the system. The 'back voltage' is directly related to how fast the motor is turning. If you put on your gloves and squeeze the end of the spinning shaft, two things will happen because of the increased load on the motor. 1.) The motor speed will slow down and 2.) the 'back voltage' will drop. Now with less 'back voltage' , the current through the motor will increase and the torque being produced on the shaft will increase. DC motors are designed to have a nearly linear relationship between torque output and current draw with as small a drop in speed as possible. i.e. more torque out = more current in.
Kirchoff has a second law which says that the current entering a device must equal the current leaving a device. With our simple heater circuit, that means that the current in every part of the circuit is alays equal.
In your example Bill, with the a resistor in the circuit with the fan motor, and we haven't changed the setting of the variable resistor or changed the battery voltage, and the resistor is now running much hotter than it did before, then we must have more current in the circuit. Given that the resistance hasn't changed and the battery voltage hasn't changed, then only thing left that could increase the current is that something is slowing down the motor and causing it to work harder. i.e. the bushings have gone dry, there is a string wound around the shaft, or maybe debris is jammed up against the fan wheel.
This will increase the current in the motor which causes more current to flow in the entire circuit including the resistor which now gets hotter.
I'll quit there since I'm sure I've already told you more than I know.
