Calibrating ADC for calibration-free temperature measurement
Yes, you can do this, but I would suggest using time rather than an ADC if possible. Particularly if you need to measure a wide range, since you'll quickly run out of resolution with a thermistor due to their nonlinearity. 

The general idea is to switch the same circuit between measuring a fairly precise reference resistor selected to be near mid-scale or the resistance corresponding to the most important temperature and measuring the sensor. That eliminates most of the errors and you don't need a precision reference voltage or much of anything else. 

You could do that with an ADC too, especially if you have access to the reference to make the whole measurement ratiometric (eliminating the absolute value of the reference). You might have issues with linearity of the ADC though, depending on how is it made. Rather than using the same series resistor (which would be, in theory, better) you could use an additional pair and tighten up the tolerance (0.1% is pretty cheap these days). 

Virtually all cheap temperature measurement circuits in consumer goods (&lt; 100°C or so) work with the time (frequency) method. 

However, based on certain experiences, I don't particularly trust thermistors at higher temperatures. You can evaluate that risk for yourself.