This is an old 324 and will never switch rail to rail, maybe 11.5v if you are lucky. There's another problem though, the 324 is used as a comparator with no hysteresis which will cause the output to oscillate (might not be visible with the LED) when inputs are near the switching point. This will be worse when there is a bit of noise as well when using long wires with the ntc resistor.
EDIT: My databook shows that with a 30v supply the output is only capable to go to 26v typically. No spec is given for 12v supply but from my experience it will be near 11-11.5v Also databook states that either input can go to +32v without damage regardless of the value of supply V+