Agreed, it won't take 3 seconds to respond to the small change in temperature required for setpoint control.... and find that the LM34's response time is very fast, almost instantaneous. I don't foresee a problem in your application.
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The LM34 might be more precise when used as a thermometer, but in closed loop apps the reading should vary between two consecutive readings only which is an infinitely small threshold. The granularity of the sensor (ie; 'C or 'F) will not affect that and both LM35 and LM34 will regulate the temperature identically around that very small threshold change....
It is also my opinion that, despite the preference of the scientific community for Centigrade measurements, the LM34 is inherently more precise in absolute terms than the LM35, simply because one degree C is so much larger than one degree F.
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