Paul,
Why do you think you need to rebuild the auxiliary thermostat? If I were in your shoes, I would test it first before buying replacement parts. You might not need to replace the slide valve (thermostat).
Things you have to consider at this point:
1). Do you want to remove the auxiliary thermostat from the car?
2). Or do it insitu?
Looking at the above picture, the thermostat (slide valve) is shown at the left side and the pressure relief valve is at the right side. Most of the time, the failure mode was caused by the slide valve (thermostat). And have not encountered one with a bad pressure valve.
Tony