Thermistor value correct on Uno backwards on Nano
There is no "correct" way. The thermistor and the resistor combine to make a voltage divider. Whether the thermistor is connected to +5V (AKA R1) or to GND (AKA R2) determines the formula to use to calculate the resistance.

The general form is:

          R2
Vout = ------- x Vin
       R1 + R2


To solve for R2 (thermistor connected to GND) you re-arrange to:

                 1
R2 = R1 x --------------
          (Vin/Vout) - 1


To solve for R1 (thermistor connected to +5V) it's:

     R2 x Vin
R1 = -------- - R2
       Vout


Vin, of course, is 5V, and Vout is a voltage you calculate from the analog reading on the Arduino.

Once you have the resistance you can then calculate the temperature. That part doesn't change regardless of the orientation of the thermistor.