You can use a higher value for your current limit resistor to limit the self heating of the thermistor. Then you can use an amplifier to get the output of your thermistor circuit boosted up to a level that your a/d converter is designed for.
A typical glass bead thermistor has a dissipation constant of about 1.5mW per degree C in still air so that's about 40mW at room temperature which means for a 10 ohm thermistor you'll want to keep the current below about 60mA.
P = I^2 * R
So for your thermistor, you'll get a signal that centers around say 0.6V which won't give you very good resolution if you are going into an Arduino analog input that expects 0-5V. I don't know what k is for your thermistor, but if you know that, you can calculate what gain you need for your amplifier. You'll want a gain that doesn't amplify the thermistor voltage over 5V at the thermistor's maximum resistance.