Instead of a digital pot simply use a set of CMOS analogue switches and a R 2R ladder network, or just a set of binary resistor values to make a DAC, and as you likely will only be using the range between 10 and 15k you can get by with only having a few values switched, to give low, 3 mid and high temperatures, easy to do with a quad switch, and appropriate resistors being switched in parallel with a 15k resistor.