Electrical – control speed of 12v dc fan with thermistor

With PWM, you have to drive the connection fully on, and fully off, each cycle.

When you have a filter/resistor on the base, you will effectively not be providing PWM to the transistor, but instead a linear control signal, and instead of being "fully on" or "fully off," the transistor will act as a voltage drop (a variable resistor) and thus dissipate a lot of heat. You're effectively building your own linear voltage regulator that way.

Other things:

• MOSFETs are better than BJTs for PWM, because when "fully on" they lose little power, whereas BJTs lose more power the more "on" they are. use an N-channel MOSFET if you can. (The BS-170 can control up to 500 mA, so it would be sufficient in this case)

• Plugging 5V out into the Vin of the Arduino is not a good idea, because there will be drop in the linear regulator of the Arduino, and the MCU will only see something less (possibly 4V or less) and be unstable. If you only have 5V, provide it to the +5V rail instead of the Vin pin.

• The 488 Hz noise you're hearing is the PWM frequency. This is because the windings in the motor, and the whole mechanics of the motor, vibrates as power turns on/off. If you need to reduce this noise, you have to push the PWM frequency up to 20 kHz or more, where you can't hear it. To do that, you may need to use a MOSFET driver circuit to drive the gate of the MOSFET, as the 25 mA or so you get out of the Arduino may not switch the gate fast enough.

A quick search led me to this:

Sense (tachometer) provides two pulses per revolution of fan. Output is open-collector and main board must have pull-up resistor to 12V.

Signal Control (PWM) is input for PWM pulses. Base frequency is 25kHz and it is acceptable from 21kHz to 28kHz. Input has TTL level and includes pull-up resistor to 5V or to 3.3V in new constructions. Signal is not inverted and 100% PWM means maximal revolutions of fan. Motherboard has open-collector type output. This construction guarantee, that with disconnected PWM signal will runs fan with maximum revolutions.

So in theory, you could use a 555 timer that produces a PWM signal based on a potentiometer input. Or simply anything capable of doing 25kHz PWM.

An example of the Triple-Five-Timer being used in such a way below. (Note that it's not from my head, found it here. Hope I didn't mess something up.) Also note, that I did not bother calculating proper values for that 25kHz operation.

^{simulate this circuit – Schematic created using CircuitLab}

Basically you adjust the discharge/charge rate of the C capacitor by sweeping the R1 pot. All there is to it. The rest is just use of the 555 magic.

That said, I'd consider replacing the transistor. That is IMO the most relevant solution.