LM35 temperature sensor strange behaviour
The LM35, like many similar circuits, is unstable with certain capacitive loads. 

If you use the 2K resistor, it must be located near the LM35 and not at the other end of the cable. Similarly the damper circuit must be near the LM35. Below is from this datasheet. 



The bypass of the LM35 (again, near the part) is highly recommended. 

These are mature parts, and they work within specifications if you follow the datasheet recommendations. Note the comment from @Hearth that the minimum supply voltage is specified to be 4V (and maximum is 30V). If you are outside that range, proper operation is not guaranteed.