Thermistor

Is the thermistor supposed to show continuity if you test it with a continuity tester? I checked the thermostats and those showed continuity but then the thermistor did not. What is the function of the thermistor?

Replace the thermister. It should have continuity. Tom ApplianceEducator.com

Yes the dryer thermistor needs to have specific amount of resistance at a given temperature or the EVENHEAT control board will not allow the motor relay to close to keep the dryer running.
Here are the components related to the symptom:
EVENHEAT control board
Motor relay
Thermistor
Below is the resistance chart of the thermistor at different temperatures:
At 50 degrees Fahrenheit the thermistor should ohm at 19.9 K ohms
At 60 degrees 15.3 k ohms
70 degrees 11.9 K ohms
80 degrees 9.2 K ohms
90 degrees 7.4 K ohms
100 degrees 5.7 K ohms
110 degrees 4.7 K ohms
120 degrees 3.7 K ohms
130 degrees 3.1 K ohms
140 degrees 2.5 K ohms