Lm35 arduino and battery
The LM35 produces an output that is 10mV per degree Celsius across a voltage supply range of 4V to 30V. This means it is largely unaffected by moderate drops in the 5V supply voltage. 

However, if your ADC reference is the +5V supply rail and this drops a volt (due to a discharged battery) your ADC "full-scale" voltage is now 4V but the LM35 output remains the same and bingo, you get a measurement error and your MCU will think that the temperature has risen above the alarm threshold.