I thought more about the alternative of putting the themistor, the potentiometer, and the gate-source of the MOSFET in series.
Reading about MOSFETs, I found that the resistance between gate and source is very high, essentially infinity.
Input resistance: The electrically insulating Gate oxide layer prevents any flow of current from Gate to Source. In a common-Source configuration with Gate as the input and Drain as the Output, the input resistance is infinity. This is because the input current (the Gate current Ig) is zero regardless of the value of the input voltage (the Gate-Source voltage Vgs). http://jas.eng.buffalo.edu/education/mos/mosfet/mosfet.html
So the voltage that the gate sees will be nearly equal to the 12v voltage drop over the entire circuit. E.g. if the thermistor is 27K ohms, the potentiometer resistance is 15K ohms, and the gate-source is ten million ohms (just to pick a big number), the voltage drop over gate-source will be 11.99v. This is higher than the threshold voltage 4.0v, so the MOSFET is "on". To get V(GS) below threshold voltage, the potentiometer resistance has to be close to the gate-source resistance. Which seems impractical. So with a series circuit, it is hard to turn the MOSFET "off".
Does that make sense?
(Sorry that you guys are having to give me a remedial lesson in electrical circuits)