Here is how to calibrate a thermistor using the log formula rather than the polynomial formula. Unlike the polynomial there are only two unknown constants so in theory you could do the calibration with only two points. What is more many thermistors come with the B value so you only need to adjust Rinf to get the correct temperature.
@Bdub has correctly pointed out that the cubic relationship is more accurate. If you calibrate the log relationship to be correct at 0C and 100C you will be 1.25C low at the mid point (for one brand of thermistor that comes with a full calibration curve). This means that if you calibrate to be correct at 20C you will be within 0.5C across pretty much the whole habitable range.