Sharing a thermister

So, do I get the TL072 input from the + of the thermistor (i.e. the field side of the thermistor), or from the MCU side which will be after the resistor (i.e. the midpoint)?

You want to measure at the midpoint as that is the output of the divider.
If you measure without the divider, you will be measuring the supply voltage on the other side of the thermistor, not what you want...

Take a look at the picture at the top of this post:
http://n0m1.com/2012/01/28/adc-battery-voltage-divide-match-and-measure/
This is for measuring battery voltage, but in your case R1 or R2 will be a thermistor and the voltage will vary with temperature.
The post explains the need for the capacitor and the math to calculate the output voltage as well...