Did you already work out the number of A/D values (resolution) per degree C you're getting with this PTC and Arduino's 10-bit A/D.
Here are the calculations for the temp range between 40C and 50C with a fixed 1k resistor.
A/D at 40C: 1185,7 / (1185.7 + 1000) * 1024 = 555.5
A/D at 50C: 1235.0 / (1235.0 + 1000) * 1024 = 565.8
A/D difference between those two temps: 565.8 - 555.5 = 10.3.
That's about 10 A/D values for a temp span of 10 degrees C.
Or one A/D value (readout/display step) per degree C.
That gets worse if you get further away from 0 degrees C.
So what are you trying to measure, and how accurate does it have to be.
Leo..