LM35: Can the LM35 suffer a low output voltage failure mode?

Hi. We have a product in development that warms an object to a target temperature and maintains that temperature. We need to ensure that risk of the temperature increasing above a limit (e.g. > +41 deg C) is acceptably low. One potential failure mode we have identified is the single LM35 sending the temperature to the CPU being damaged or simply developing a fault so that the output is low, either with a DC offset or reduced gain. This would mean too much heat energy is applied and the temperature limit exceeded. We have not seen this failure and it is only a hypothetical risk. Can you please tell me if the LM35 is known to produce a low output voltage under any circumstances, such as ESD damage or other causes? For the record, our sensor is potted onto the monitored component and connected via a cable (tens of cm) to the control PCB and there to an ADC input via a series 2.2 kohms and 2.2 nF capacitor to 0V.