What's wrong with my thermostat (fan / limit control)?
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.