(help) Control a 3-pin PC fan

Thank you for the information and your time.

For sure when I supply with less voltage it stalls.
My initial intention was to read a NTC temperature and set a gradual increase in the pwm of the fan (from arduino) parallel to the temperature increase,(or even with the temperature acceleration increase), but now my plan has changed, and probably I will use this

as it is just a simple analog circuit wich i've used lots of times in the past. It seems history wants me stucked in the past.

About the tacho, thank you for verifying my doubts , as I wasted 2 hours by testing several fans / codes / layouts to realise that the yellow wire is not pwm input