I´am using the OP177 to amplify the Vout of the LM35. The obtained resolution is very near to 0.01ºC (0.0001V) with a ADC of 10Bit, 0-2.5V. Without the amplification the resolution is pproximately 0.06ºC
In the measurement of CPU temperature is a relativity problem because the measurement scale is reduced to 40ºC, but for the rest of measures (11 channels) of the system it would be sufficient.
The solution would be obvious to reduce the resolution in this channel (smaller amplification) or to reduce a fixed tension. For example -150mV (15ºC), it would increase the scale of measurement.
Here some images can be seen about my system, and this link
NTC NTC2 if possible that interesting for you.
Still I have left tests to do. Sorry my bad english