Looking at your thermostat specs etc, I assume it is a basic bimetallic rotary spring operated mechanism with manual SPST switching. since you can operate it to "on" and you know the contacts close in manual mode, and when physically turned/twisted, I suggest a couple of tests to verify operation of the bi metal spring. Disconnect the electrical power. Use an air heat gun to blow on the sensor unit and watch to see if actuator moves in the switch housing as you would expect. Connect an Ohm meter across the load/fan terminals. As the temp rises, the ohms should change from infinite/open to 0 ohms/closed when contacts close at the set limit. Although this is not a calibrated test, it will verify that the spring is responding to temp changes. If this test works properly and you are satisfied the unit is working, I may suggest you look at where you are trying to sense the heat from the wood stove. It may be that the area you have selected to mount the thermostat is not seeing enough heat from the stove. you may have to monitor the temp closer to the flue or at an area that radiates heat better. You may also have to fabricate some type of small plenum directly on the surface of the stove for the sensor to mount into. In that I mean just the spring/temp sensor assembly, not the actual electrical switch assembly. Good luck.
Check your set points. You'll want to have a degree or two between the heating and cooling set points. For example, if your cooling set point is 76°F, you'll want to keep the heating set point at or below ~74°F. Check the documentation for your unit, to determine the recommended buffer value.
Also note that some units allow you to program the swing setting, which determines how far off from the set point before the unit signals for heat/cool. For example, if you have a heating set point of 68°F, with a swing setting of 1°. The heating system will be signaled ON when the temperature is 67°F, and signaled OFF at 69°F.
In the above example if you had the cooling set point set to 68°F too, you'd end up fighting for control. Heat would bring it up to 69°F, then cooling would kick on and bring it down to 67°F, then heating would kick on and bring it up to 69°F...
I'd try to keep a buffer of at least 1°F. So if the swing is 1°F, you'd set heating to 68°F and cooling to 70°F. Some documentation recommends only a single degree (heat=68°F, cool=69°F), but I'd recommend keeping at least one degree between the set points.
Best Answer
There should be a notch, slot, groove, or other marking on the shaft. Which should align with a similar marking on the knob.
If not... Simply turn the shaft to one of the extremes (all the way up or down), then install the knob to indicate the appropriate setting.