How to relate voltage Output to temperature with a Wheastone bridge
You're missing a trick if you make R4 to be 20k.

The log(ish) law of most thermistors affords a nice cheat. If you make R4 to be equal to the thermistor resistance at the middle of your temperature range, then the voltage out of the R3/R4 junction is very linear with temperature over +/-5 degrees C, and not far from linear over +/- 10 degrees.

If you want to exceed that range, then you'll need to bite the bullet and work through what the thermistor resistance means for the output voltage at any given temperature. When you buy a thermistor, you'll be told the parameters of the Steinhart-Hart curve. Alternatively, take measurements of resistance at several different temperatures and fit the curve.

Although it looks fearsome, the Steinhart-Hart curve is easy enough to whack into a spreadsheet to get resistances, and then another column will give you divider output voltages. Either fit a simple curve to the range you're interested in, or pick some specific points that are close enough together so that linear interpolation doesn't cause too much error, and put a table of those in your Arduino.