I have a soldering pencil which has an integrated PTC RTD built in. The temperature of the RTD can be represented using this equation y = 0.0056x^2+4.9382X-239.43 where x is the resistance of the RTD and y is the temperature in Celsius. The resistance would vary from 50 to 100 ohms (its a relatively low resistance for an RTD).

Could you please provide me with a way to measure the resistance of the RTD giving the greatest resolution to the arduino measuring it? (ie use all 1024 voltage levels measured with the arduino's analogRead() )

You would not get much better resolution, if you 'd carefully scale input to 0-5 range using OPA, compare to simple R - RTD voltage divider.
Other options, use external ADC, 16 - 24 bits, or you may dig for Atmel app. note explaining oversampling technics AVR121.
For update rate 3 Hz , which is (IMHO) o'k with temperature measurements, they give this numbers:

Voltage Oversa- Right Ideal Ideal voltage Maximum
resolution mpled shifted decimated representation Bandwidth
result