Equation to calculate voltage divider resistor value for an input of op-amp
You can prove this by writing an equation for the difference of the two voltages and setting the derivative to zero. 

\$\frac{V_{DIFF}}{V_{CC}}=\frac{R_X}{R_1+R_X} - \frac{R_X}{R_2+R_X} \$

Differentiate (and set to zero) and you get: \$\frac{R_1}{(R_1+R_X)^2} - \frac{R_2}{(R_2+R_X)^2} = 0 \$

Simplify and you get Rx = \$\sqrt{R_1 \cdot R_2}\$ 

Given the fixed percentage change of thermistors per degree this will also maximize the voltage change per degree at the extremes (making it equally bad at each end, compared to best which occurs at the center of the resistance range- when the thermistor resistance equals the series resistor). 

Edit: The principle behind setting the derivative to zero is that this will detect maxima (or minima). You have to apply some thought to ensure you have a maxima and to eliminate the constraints (if any) as potential points. This is a standard technique. 

As to the calculation, the quotient rule makes easy work of differentiating wrt Rx and the rest is just algebra.