To measure temperatures in the higher end you have to lower the value of your series resistor (now 100k) to roughly match that of the thermistor (you mention a resistance of about 2k). That will greatly improve your accuracy measuring the resistance. Just do the math, and see the effect of one ADC point difference at a ratio of 100/2 and 2/2 (or 100/100).
As a rule, when using thermistors, you should choose a series resistor value that matches the value of the thermistor at the temperature of interest. That gives you the best accuracy at that temperature.