Oversampling, additional bits and a thermistor
Oversampling and averaging can get you more resolution, under certain circumstances, but it's not a magic bullet.

If the noise at the ADC, either inherent in the system, or indeed added externally for the purpose, spreads the input signal suitably, then adding together N readings and averaging will improve the SNR by sqrt(N). 'Suitably' means either a flat distribution of exactly 1 LSB width (which is difficult to arrange and maintain) or a normal(ish) distribution covering 'several' LSBs (rather easier).

While this improves the signal to noise ratio and so the resolution, it will not improve the accuracy. It does nothing to improve low order non-linearities in the ADC, and nothing to improve its drift.

Generally if you are using the ADC to make fine distinctions between similar voltages at similar times, then it's well worth doing. If you want to make accurate differences between widely different voltages, or over a long period of time, you probably need a fundamentally better ADC.

It really depends what the limiting factors are in your ADC, and how you want to use the reading, whether the extra bits you get from oversample and average are useful or not.

Using the inherent noise of the ADC and then averaging a few readings is a very easy thing to do. It's worth doing the experiment to see whether the averaged ADC really gives you a benefit in your use case.