Using a mercury thermometer is permissible on Shabbat (using a digital one is not).
There is a special mercury thermometer as well meant for measuring basal body temperature, which is available in most pharmacies. This is what you should use for Shabbat. As no two thermometers are exactly the same, and accuracy is important, we suggest using both the mercury and digital thermometer for a few days at the same time, in order to see the difference between the thermometers. In this way you can calculate what the number would be on the electric thermometer had you used this on Shabbat, but actually measure with the mercury thermometer.
Furthermore, there are additional signs of ovulation that one can learn to recognize such as the changes in cervical fluid. We suggest that you consult a
fertility awareness counselor for training in this. Knowing two signs increases the accuracy of the information. Checking cervical fluid is not a problem on Shabbat.
Behatzlachah!