Can I improve the accuracy of LM35 temperature sensors by averaging several sensors?
You can not guarantee more accuracy, but you can possibly get better signal to noise ratio.
Imagine if all the sensors were off by the same amount as allowed in the specs. Averaging them would not yield better accuracy. If you had a reasonably large number of these sensors and they had a random error distribution within their allowed error band, then you would get better accuracy by averaging. However, the problem is that you have no way of knowing if you have the first case or the second. If all the units are from the same production lot, their errors are likely not randomly distributed.
The noise does go down, however. Each sensor adds some noise to its reading. This is uncorrelated with the noise from the other sensors, so averaging does lower noise. Of course this is not true of noise coming from outside the whole system since that would be correlated and averging the multiple sensor readings won't reduce it.
Note that there is more than one way to "average". You are thinking of averaging accross multiple sensors to reduce noise. However, since this noise is essentially random, you can just as well average between multiple readings from the same sensor taken at different times. In the more general case, this is really low pass filtering. Since temperatures change slowly, aggressively low pass filtering the output of a temperature sensor does reduce noise. Looking at this in frequency space, you know the temperature changes slowly so high frequency components are noise and can be safely attenuated.
Yes, using multiple sensors can give you an average temperature. How correct that temperature is still at question.
If 50% of the sensors are above the real temperature, and 50% are below, then you will get the real temperature (or as good as). If 75% are above and 25% are below, then you will reading the temperature as higher than it is.
For accuracy you will need some reference to test the sensors against to get the real temperature - usually a known temperature to calibrate the sensor against.
As for the noise cancelling, you can do the exact same thing with one sensor and sampling it multiple times and averaging the results.
If the errors were random you could expect an improvement of about a factor of 3 for 10 sensors (the square root of 10). But it is likely there are systematic errors which wouldn't cancel.
Why do you want better precision than 0.5°C in the first place?
Which temperature do you want to measure? If you have ten sensors they won't all be in the same place. Most of the time it will be better get a higher precision one.
Do you even have space for 10 sensors?
It is a good idea to do multiple readings of one sensor.