Electronic – Controlling heat gun’s element: where to put SSR without disturbing motor

I'm working on a pet project of mine, creating a coffee roaster, where I'm using a heat gun as the heat source. To improve my control of the heat output of the gun, I've set up an Arduino to control a solid state relay (SSR), that in turn (if I get it to work) should control the heating element of the heat gun, by switching it on and off in intervals (high power => longer periods of on, low power => longer periods of off).

Now.. For this I bought a very simple heat gun with two settings – high (high temp, high fan speed), and low (lower temp, lower fan speed). I opened up the heat gun, and it seems that the motor circuit (AC->DC rectifier + motor) is using the heating element as a resistor(!). This means that I'm not able to isolate the circuit for switching heat on/off from the motor.

I've tried to make a circuit diagram (I'm not an electrical engineer, hopefully it's understandable anyway). I THINK I've managed to get it fairly correct.

In this diagram, the whole motor circuit including rectifier is the "M". The heating coils is divided into three. I've attempted to figure out the values as well by measuring and some calculations:

• R_a is the largest and is used both on setting 1 and 2. I believe this to be 22 Ohms.
• R_b is only used on setting 2 and is a small section of the same coil as R_a. Think this is 27 Ohms.
• R_c is a thinner, smaller coil used on only setting 1 (lowest). I believe this is 26 Ohms.

(PS: Take the Ohm values with a grain of salt – but they seem to check out)

My question is: Is there any hope for me to connect my solid state relay to control ONLY the heating coils, without disturbing the motor? I don't really need the lowest setting – I'm going to use the fan on highest, and simply control the power to the heat coils using my SSR.