I would try a 25 turn 50+ohm trim pot, as this would give you a good range of temperatures while still giving you a fine adjustment at the values your wanting.
Something like this:
http://jaycar.co.nz/productView.asp?...T&SUBCATID=803
Using the rule for resistors in parallel;
1 / R = 1 / R1 + 1 / R2 + ......
where R = the resistance we want/the chiller setting (ie 8 Kohm @ 20c) and R1 = the resistance of the probe at running temp (ie 15 Kohm @ -17c) and R2 = the resistance of our trim pot, we can now find the minimum resistor size needed.
1 / 8 = 1 / 15 + 1 / R2
R2 = 1 / (1 / 8 - 1 / 15)
= 17.14 Kohm
if you want flexibility you want a larger resistor as the more resistance you add the closer you will get to the original value but the more sensitive the adjustments become as a much larger range has to be moved through in the same number of turns of the trimmer (ie 25 turns 0-XX ohms).
Some examples of probe resistances when the trimmer is set to max and the controllers trying to hold 20c (8 Kohm);
R1 = 1 / (1 / 8 - 1 / R2)
25 Kohm: R1 = 11.76 Kohm
50 Kohm: R1 = 9.52 Kohm
100 Kohm: R1 = 8.7 Kohm
so you can see that if you had a 100 Kohm trim pot set to max with the controller set to 20c your temp would be about 15c, where as with the same setting and a 50 Kohm trim pot the max temp you could adjust to is about 9c, and with the 25 Kohm about -4c.
Something some people like to do (I don't bother TBH) is use a resistor in series with their pot (which are both in parallel with the probe) to act as an adjustment safety eg put a 15 Kohm resistor in series with a 50 Kohm trim pot that way your resistance range becomes 15-65Kohm (17-9Kohm on probe with cont @ 20c) giving a temp range of about -24c - +12c while preventing anyone accordantly adjusting the pot to 0 ohm shorting the controller.
Replacing the thermistor is a viable option however you are limited to the range of temperatures settable by the controller also that range might be affected but the resistance/temperature gradient of the thermistors response.
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