Step 3: What is a Voltage Divider?
In short, if you have two resistors in series, the voltage drop across each resistor is in proportion to the size of the resistor. If you have Voltage V across a circuit of R(1) + R(2), then V = V(1) + V(2). So if V=3V and V(2) = 2V, you know that the V(1) = 1V.
Now the basis of Ohm's Law is that the current (I) is V/R. In a series circuit, the current is the same throughout, so the current through A and B is the same for the whole circuit. Therefore I = V1/R1 = V2/R2.
We know V2 = V - V1, Plugging in, we see V1/R1 = (V-V1)/R2. Solving we get R2 = R1*(V-V1)/V1
So if know if we know V(1), V, and R(2), we can solve for R2.
If we have R2, we know the value of the Thermistor!