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Yes it should... But if the voltage is too low it may not.
if your output is too low... add the ADRESH to a known voltage... ie... we know room temp is 0.48v.. ish, so start at mid point say 128 then add the ADRESH to it to see if there is any discernible change in speed on the motor... If not then double the ADRESH before adding.. Very soon you will see changes to the motor, even when you touch the temp sensor.
I'm sorry yours is 10mV per C I was thinking it's the same as the 9701 which I've use a bunch of. But that makes it worse room temp of 70 ºF is only 210mV
So you need to take your reading and scale it by 10
Read the output on pin 6 and see what it is I bet it's too low to turn on the transistor your not even getting a volt there and you have a 2.2 k resistor no way that will turn on the base of the transistor change the resistor to 560 ohms or a 470 ohms and you may see the thing move the motor
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