LM35 gives very high values in room tempratures, and decreases when we exposed it to a heat source!
If you want to see why more noise clipping from oscillations causes a lower DC voltage see here.

Datasheet says:


  The low-output impedance, linear output, and precise inherent calibration of the LM35 device makes interfacing to readout or control circuitry especially easy.


The more you follow TI’s Fig 12 or 13, the easier it gets.

http://www.ti.com/lit/ds/symlink/lm35.pdf


or Fig 2,3 from  https://www.jameco.com/Jameco/Products/ProdDS/1276463.pdf. But TI now owns NSC .


To maintain low impedance , long loose wires are not allowed due to antenna effects picking up noise.

The signal wires must be coax or STP (shielded twisted pair CAT5,6) or just UTP for short distances. Floating grounds and Common Mode (CM) noisy SMPS can be suppressed further with >1nF from 0V to earth ground but if above is properly routed not essential.   

Cable length matters so use STP if in doubt. Then read more about shielding.

Don’t forget to include a small 0.1uF Vcc cap near the sensor. Then add either series R or shunt RC before long cable.  0.01uF is marginal and 10pF does nothing at 100kHz to lower impedance. But it must be done at source.

The reason it fails is because it has a Source Follower like emitter follower that can oscillate near 100kHz (here) with the large cable capacitance load (100pF/m ~) without either raising the series R or drowning high f currents with low R big C in shunt.