Why LM35DZ temperature sensor accuracy deteriorates towards the lower end of the range?
Have you actually measured the voltage the LM35 is outputting with a multimeter? I would trust the LM35 far more than the ATmega's ADC to go completely down to 0&nbsp;V.

From the graph you included, it looks like something is hitting a rail somewhere. 

If it is indeed the LM35 outputting the errant voltages, try a pulldown (~50&nbsp;kilohm?) on the output to ground (or better yet, -5&nbsp;V).

You're measuring a very small voltage with the built-in ADC - 20&nbsp;°C is only 200&nbsp;mV. Furthermore, without a negative power rail, the sensor is only really good to 2&nbsp;°C, and any bias current on the output (from the ADC) will probably affect the readings you get.