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For most popular lcd modules, it has to be connected between the LCD contrast pin and ground.One pin of the resistor connects to Vcc the other to the input of your LCD.
Using the potentiometer, change the resistance until the contrast is what you want. Then turn the power off and connect a multimeter to calculate the resistance for your selected contrast. Place on probe on the pin connected to Vcc, the other to the middle pin. Or you can place one probe on the middle pin and the other on the pin connected to ground and subtract from 10K ohms. If you want to replace simply replace the potentiometer with the same value of resistance (or closest value to it). One pin of the resistor connects to Vcc the other to the input of your LCD.
Good luck
In contrast to resistance thermometer, that has a fairly linear characteristic, all thermistors have rather non-linear behaviour. In a small temperature range, a linear approximation may be sufficient exact anyway. See a brief overview of expectable characteristics:Do all thermistors have linear relation between temperature and its resistance
the linear approximation (above) works only over a small temperature range