Electronic – analog circuit to convert one resistance to another

While I agree with Rocketmagnet's schematic (though I would decrease R4 to 1k\$\Omega\$) I can't agree with his calculation of resistor values. Copy of the schematic:

Rocketmagnet calculates for two different voltages on pin 3 of the comparator, which should represent the hysteresis. However, at both toggle points this voltage is the same, namely the voltage set on the inverting input using the potmeter.

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The confusion stems from the fact that the hysteresis feedback is added to the signal, rather than the reference voltage, which you would normally do. The consequence is that despite the hysteresis we only have one reference voltage: the voltage at the potmeter's wiper. A more common way to solve this would be to connect the potmeter with R5 to the non-inverting input and the signal to the inverting input. But we'll see that this works too.

Let's suppose the potmeter is set to 2.5V (could have been done with two resistors), and that the comparator's output swings between 0V and +5V (\$V_{CC}\$). The comparator should have a push-pull output. The comparator's output should go high when the NTC's resistance is 845\$\Omega\$. Until that moment the output is low, so that

\$ R5||R2 = 845\Omega\$

to let the non-inverting input pass the 2.5V toggle point. Likewise, the comparator's output should go low when the NTC's resistance reaches 860\$\Omega\$. Until that moment the output is high, so that

\$ R2 = 860\Omega||R5 \$

So we have the following set of simultaneous equations:

\$ \begin{cases} \dfrac{R5 \times R2}{R5 + R2} = 845\Omega \\ \dfrac{860\Omega \times R5}{860\Omega + R5} = R2 \end{cases} \$

which gives us

\$ \begin{cases} R2 = 852\Omega \\ R5 = 96.89k\Omega \end{cases} \$

Use a microcontroller to measure the thermistor, then program a lookup table and make it control an electronic potmeter. Intermediate values can be calculated by interpolation.